Back to the subject in hand !

Carrying your rig is fine but some airlines have been difficult about AADs, especially if you have a Cypres rather than the old spring-loaded cable type. because if it's armed and your aircraft makes a sudden pressurisation adjustment as it descends, the AAD could fire and operate the reserve ! The Cypres also, as you are probably aware, activates with a (very small) explosive charge which upsets some carriers.

Apparently different airlines have different rules, and they are not well publicised. Just call the airline and ask.

http://www.skydivingmagazine.com/ques10.htm#Taking Rigs on Airliners