Just seconds after the matinee showing of “La Bohème” at the Metropolitan Opera last Saturday, a crew of stagehands began dismantling the magic.

Neither Marcello, played by Peter Coleman-Wright, nor Mimi, played by Angela Marambio, had slipped through the curtains for applause when the stagehands split apart the set’s Parisian roof apartment and began carting it away section by section.

It was 4:30 p.m., just three and a half hours before “Madama Butterfly” was set to play for its last night of the season. In that time, the two-story sets of “La Bohème” had to be stored for Monday’s show and the stage transformed into yet another illusion of time and space.

An assistant head carpenter, Robert Carlson,52,called it “organized chaos.”

“I think of it like one of those old thumb puzzles,” he said.

For a crew of about 30 carpenters, electricians, and prop men, the task comes about weekly. Each Saturday, the Met puts on one opera in the afternoon and a different one in the evening.

Working in unison, the stagehands are in one moment carpenters, plucking out pins that hold the set together called”20 penny hinges,” and in the next, they are seafarers on an old ship, rolling up cycloramas, or “sykes,” that look like massive sails. Mr. Carlson and other veterans of the Met’s backstage lead the men, and when something goes wrong — which is nearly inevitable — they improvise.

Props, pieces of scenery, and netted curtains with paint called “scrim drops” can go in any direction. They can be hoisted up close to the ceiling, 120 feet off the ground. They can be lowered 35 feet to the basement, known as “sea level,” by a massive hydraulic lift in the called “20 penny hinges,” and in the next, they are seafarers on an old ship, rolling up cycloramas, or “sykes,” that look like massive sails. Mr. Carlson and other veterans of the Met’s backstage lead the men, and when something goes wrong — which is nearly inevitable — they improvise.

Props, pieces of scenery, and netted curtains with paint called “scrim drops” can go in any direction. They can be hoisted up close to the ceiling, 120 feet off the ground. They can be lowered 35 feet to the basement, known as “sea level,” by a massive hydraulic lift in the center of the stage floor or the “scenic elevator.” They can be pulled into cavernous areas to the left, right, or back of the stage on motorized wagons or moved onto trucks on Amsterdam Avenue through a shipping dock at the back. Three to five trucks come in and out every day, taking pieces away and bringing others back from a storage house in Newark, N.J.

Last Saturday, the pieces were moved around like a giant three-dimensional game of Tetris. As the hydraulic lift raised three stories into the air, men pulled out pieces of the wooden floor from “Madama Butterfly,” while others slid the second story of the Parisian buildings from Act II of “La Bohème” onto the raised platform. To the left and right of the stage, bigger pieces were split into smaller parts and stowed tightly in every shape of space.

There is no master script to follow for the construction of a set. Rather, the formula for setup is mostly memorized over time by senior stagehands. Pieces are aligned with one another by initials and words. One piece for the floor of “Madama Butterfly” was marked: “Pale, Te, Ride, Ac, Bk, Stink, Mt, Jb.”

Even while more massive work is done, there is attention to detail. One man carried a magnet mounted on a pole to pick up fallen pins and other metal objects, while another vacuumed what was left of the snow from Act III of “La Bohème.” Just before “Madama Butterfly” was set to start, men wearing protective foot covers gently polished the wooden set floor with mops.

The stagehands range from “generals to lieutenants to colonels on down,” another assistant head carpenter, Louis Pavone, 61, said. They look like engineers and carpenters — some have tattooed arms, gold crosses, and wear Tshirts that read FDNY or IATSE Local 1. Others wear button-up, short-sleeve plaid shirts. Almost all carry screwdrivers, hammers, and a pouch filled with 20-penny hinges, which look like nails bent 90 degrees. During lulls they play “lunch box lotto,” where one person sells raffle tickets for $10 or $15. The winner takes home a few hundred dollars.

Mr. Pavone, who leads with a taciturn kind of authority, joined the Met’s backstage at the age of 22 in 1967. This is his 39th season. In those years, he has heard hundreds of operas, some of them in three or four versions. Still, amid all the repetition were moments that stuck out, he said.

There was the time when Luciano Pavarotti and Placido Domingo took turns singing a part of a scene in “Trovatore,” or when Franco Corelli sang a perfect aria in the third act of “Tosca,” he said.

“When something happens, you get a chill up your spine,” he said. “You know something good is happening.”

During the opera season, stagehands work behind the scenes nearly 24 hours a day. On Saturdays, the day crew arrives at 9 a.m. to set up the first opera. It leaves after the last act of the second opera around 10:30 p.m. The night crew arrives at 11 p.m. Crew members take down the night’s show and prepare for the next day’s opera until 7 or 8 the next morning. On weekdays, another crew works in the electrician’s shop, welding pieces for new shows and repairing old ones, as well as building other mechanisms and light setups.

At any one time during the season, four operas play in the repertory. At the same time, at least one and sometimes two other operas are in full rehearsal. It is these five to six productions that are constantly moved around behind stage. In the summer, smaller crews work on building the sets for the next season and practicing how to build them in short periods of time.

Surrounding the stage area, including the massive storage spaces, are offices and workshops all connected by narrow stairways, hallways, and elevators. Every spot is a mixture of the thick wires, carefully crafted set pieces, and the lives of the men who work there. One corner held a Parisian wall with an antique poster resting against a work area composed of computer consoles and a pinup of a scantily clad woman from a magazine.

The basement, “sea level,” is an icy, mysterious place that has the feeling of a submarine engine room. Even in the middle of towering wooden set pieces, the glowing, translucent centerpiece of “The Magic Flute” seems to need only a single actor to bring it back to life.

The job is not for everyone. Some of the stagehands stay for a few months — but the ones that stick around tend to develop at least a little taste for the opera. As they work, Mr. Carlson said, some have been known to whistle a little tune from “Aida,” or “Tannhäuser.”

“It comes through by osmosis sometimes,” he said.