This happens to be an incredibly busy week for me, so I simply don't have the time right now to give you a long, detailed answer up to the standards of /r/AskHistorians. That said, I have a huge library of New York City history books so I can give you some good recommendations for further research:

• Critchley, David. The Origin of Organized Crime in America: The New York City Mafia, 1891-1931
• Dash, Mike. The First Family: Terror, Extortion, Revenge, Murder and the Birth of the American Mafia
• Dickie, John. Cosa Nostra: A History of the Sicilian Mafia
• Ferrara, Eric. A Guide to Gangsters, Murders and Wierdos of New York City's Lower East Side
• Hortis, C. Alexander. The Mob and the City: The Hidden History of How the Mafia Captured New York
• Pietras, David. Made in New York City: A Journey into the World of the New York City Mafia Families
• Raab, Selwyn. Five Families: The Rise, Decline and Resurgence of America's Most Powerful Mafia Empires

I hope those recommendations point you in the right direction. I am sorry I couldn't be more help; if I can find some time later on, I'll try to answer your question properly.

I'd like to see an answer to this too. Paging /u/discovering_NYC, newly flaired specialist on NYC history!