The book is ambiguous as to how the war was fought. Sonny's attempt to take out the heads of the other families implies that they were all combatants, but the peace conference chapter just says Barzini supported Tattaglia "with money and influence." There's no reason to think of Cuneo and Stracchi as combatants, except that the war was called "The Five Families War." On the other hand, it's hard to imagine Phillip Tattaglia holding the line alone against the Corleones for any length of time.