It is said that the Mob helped the US during the conflict with Cuba. How did the US get in contact with the mob? Instead of arresting them? Did the Mob see an incentive to help the government?

Not sure about Cuba specifically, but in Sicily during WW2 the Allied Forces did the same thing. The essential pieces of the puzzle were aid (ie bribery) and clemency. Mafia members we already had hands on were offered better deals or even early release in exchange for cooperation, while extant mafia members were contacted through intermediaries and offered money, resources, and/or weapons for cooperation.