No one knows exactly why 29-year-old Iranian costume design student Mahtab Savoji turned up dead in the Venice lagoon last week. Her body, nude except for a string of pearls around her neck, got tangled up between two water taxi drivers near the Via Cipro dock in Venice Lido on January 28. After fishing the corpse out of the lagoon, a Venetian coroner determined that the woman—then unidentified—had been strangled to death at least 24 hours before her body was thrown into the murky water. Her lungs did not contain water from the Venice lagoon, and her body showed no apparent signs of violence other than strangulation. But no one knew who she was or why she was there.

Meanwhile, 250 miles away, the day after the mysterious body floated to the surface of the lagoon, Savoji’s friends in Milan—where she had shared an apartment with two hospitality workers from India since November—were starting to get worried. Savoji hadn’t been answering her cellphone, which wasn’t like her. She missed a Tuesday appointment at the school where she was studying costume design, which tipped off her friends that something might be wrong. When she missed another appointment later that day, at the Iranian social club where she and other friends from Tehran gathered for fellowship, her friends called the police.

It took nearly a week to link the floating cadaver and the missing Iranian. But on Monday, police arrested Savoji’s Indian roommates on suspicion of murder. According to the reenactment of the crime provided to the press by police in Milan, Rajeswhwar Singh, 28, his girlfriend Gagandeep Kaur, 30, and Savoji were either engaged in an erotic game that went terribly wrong, or Savoji refused an invitation to join her roommates in some sort of ménage à trios that wasn’t meant to be. Sing and Kaur, according to police, confessed that around 2:30 on January 27, they “accidentally” strangled Savoji to death and panicked before stuffing her into a large pull-type black suitcase. They then took the train, lugging the heavy suitcase, to the nearby town of Lecco with the intention of dumping the body in Lake Como, police say. But the lake town was packed and they couldn’t get rid of Savoji’s body there. They allegedly then took a six-hour milk run train—with the body inside the luggage in tow—through Milan and on to Venice where they were captured on CCTV footage struggling to pull the heavy roller suitcase through the Santa Maria Elisabetta square not far from Venice Aiport. They then hopped on a vaporetto, or water bus, and headed Venice Lido, where they reportedly copped to dumping the body with the hopes that the currents would drag it out to sea.

The two then grabbed a bite to eat in Venice and hired a taxi to drive them back to Milan for €500, according to Italian authorities. The taxi driver who is cooperating with the police investigation, called “Giampaolo” in court documents, described their behavior on the long drive back to Milan as “tranquil.” He said that they slept all the way from Venice to the outskirts of Milan. “They didn’t seem nervous or worried,” he told police, according to public records associated with their murder arrest. “They told me they missed their train and asked what it would cost to drive them to Milan.” The driver said he quoted them €600 but eventually settled for €100 less.

The pair allegedly arrived back in Milan a few hours before Savoji’s nude body was discovered in the Venice lagoon and went about their usual business. Singh worked as a doorman in a local hotel and Kaur was a waitress. Once the police connected their mystery cadaver to Savoji, they started investigating the disappearance before questioning the Indian couple, apparently trying to catch them in a trap. Wire taps caught Singh telling his girlfriend, “We need a lawyer,” according to police records filed to preliminary magistrate Giovanni Zorzi, who is leading the investigation.

According to the initial police dossier, neighbors who lived on the Via Pericle near the threesome reported hearing strange noises and angry arguments among the tenants. Savoji had arrived in Milan in 2012, but she only moved in with Singh and Kaur in November. Apparently they had a difficult time keeping tenants to sublet the back bedroom of the apartment, according to neighbor testimony. Savoji’s friends reported to police that she had complained that Singh made frequent passes at her in front of Kaur and that on numerous occasions they tried to forcibly invite her to their bedroom. One neighbor reported that just weeks before Savoji was murdered, she heard “screaming and objects being thrown” in the sixth floor apartment. Singh apparently told the neighbor the next day, “When I get angry, I lose all reason.”

Another friend of Savoji, whose name is not listed in the police records, apparently told police that Savoji was increasingly uncomfortable with her living situation. “She was desperate to move and had given her notice to vacate the apartment,” the unnamed witness said, according to police records. “She feared something terrible would happen.”