I'm familiar with the Cleveland family's history with the Teamsters Union. But just the sheer size difference (both family and locale) of some of the families in NY and Chicago would, in and of themselves, make them more influential in the Teamsters Union than a mid-size family like Cleveland. The Genovese family, for instance, had influence or control over Teamster Locals 97, 145, 191,560, 701, 807, 808, 814, 843, 945, as well as Joint Councils 16 and 73. I'm sure I'm missing others. I've also read statements in the past from law enforcement, prosecutors, as well as former mafiosi saying the Genovese had the most clout in the Teamsters Union. And, of course, Cleveland answered to the Genovese.