The Calabresi mobsters are archenemies of Fat Tony's, that tried to kill him.
The Calabresi mob is lead by Mr. Calabresi. When Calabresi goons see Fat Tony driving children home from school, the goons try to kill them. However, Fat Tony uses a three-ring binder to puncture the goons’ tires. They crash into a baking soda truck, and then they're hit by a vinegar truck, which they say is not that bad. Then a TNT truck crashes into them, causing an explosion, setting the vehicles ablaze.
They later are shown attending a sit-down with Fat Tony and his mafia. Fat Tony's son Michael brings them in soufflés he made, making Fat Tony appear weak in the eyes of his enemies, so they try to kill him again. It almost works, as Fat Tony is wounded and out for three months.
Bart and Homer get sick and twisted, and potentially very violent, so Michael declares they're getting out of the mob business. He invites the Calabresi mobsters to dinner, and tells them he's handing over all his father's territory in exchange for the safety of his family, and the Simpsons. However, he serves them each a plate of poisoned spaghetti, killing all three.