I got to read it again, but in the book SuperMob, it states that a lot of the people that made L.A. what it is, actually came from the west side of Chicago. Like a lot of the big movie guys and stuff.
I think this is where the deep Chicago connections come from, more so than the Italian mafia, it's more about the Jewish contingent.... I think..
Doc Stacher, a Genovese associate who was really close with Zwillman, Catena, and Lansky, was a silent partner in Columbia Studios.
https://en.wikipedia.org/wiki/Joseph_Stacher
