From available info there wasn't really one with the exception of the Genovese Family which had historical ties with NOLA through Costello and Kastel. Later on there were family ties between Fat Dom Alongi and Frank Gagliano (cousins). But in general it seemsthey each stayed out of each others affairs. I'm sure there were occasional contacts between them for whatever reason (other than La Stella in 66) but have never come across any info of any problems.