(and a ban on mw3, BO, BO II seems ban for all of them)
This is false. TAC bans do not carry over to all of the TAC covered games. VAC bans do not carry over to other games unless they are Valve Source games. check facts next time. You can be banned in BO2 or BO and still play the other one. MW2, MW3 all have seperate banning systems so if you are banned in 1 you can play the other. I am speaking from experience.