i assume you mean 580exII. are you shooting ETTL or manual? ETTL won't mix well when adding a strobe. your camera won't be calculating all that extra light from the strobe.
the AB's have an optical trigger on them so technically the 580exII can trigger it. you'd set both the 580exII and AB manually. it gets messy once you want to add your 430ex into the mix. the speedlites need to communicate via the preflash which could set off the AB. sync cables would work, but it gives you something to trip on and you're still setting everything manually. instead of sync cables, you could buy some radio triggers for a wireless solution.