There we at minimum 3 sides.
1) Anti-Nation forces.
2) Nation sympathizers / CH.
3) Third parties: at minimum PL / NC
The first cyno that went up was for Nation reinforcements in the shape of a Nyx and 2 triage thannies to support Ghost Hunter.
The second cyno was for a titan bridge of the CH subcap fleet that was on standby to support the Nation sympathizers.
The third, forth and fifth cynoes were others: one was used by USF who - to the best of my knowledge - were supporting the cause of fighting Nation and I believe PL and NC used separate cynoes as well as it would appear to me from looking at the killmails they got that they most probably were in separate fleets and on separate comms.
The grand total of PL / NC supercarriers that jumped in was approximately 20 and they engaged the Nyx that was with the Nation sympathizers.
Shortly after everyone bailed, the only thing CH took care of quickly before pulling back to regroup was taking care of the HICs to allow the friendly Nyx that was dropping quickly to escape from the PL/NC forces.
After that everyone scattered, PL / NC took out some NC caps and various battleships they could get tackle on.
Until DT hit the fighting spread throughout the entire system, around all celestials, and continued at a smaller scale as people chased each other picking off the confused ones that didn't know what to do.
Edit: Coolness - I just found out there is stuff to watch of this.
http://dl.eve-files.com/media/corp/NamNam/nyx_gets_out_25may2010.mkv