Regardless of which airline you use, it's the airport I'm usually concerned about.
So if Zumi flies in as "checked baggage" (this airline term for pet travel disturbs me since they are living beings not objects), he will be unloaded and go in the Baggage Claim area - where the "oversize" baggage is (near those things that go round and round; this is usually where skis, golf bags, etc are claimed).
Make sure you get there early (at that (Oversize) Baggage Claim area). I'm not sure where this is located in LAX or Burbank Airport but from my experience at SFO, while there are airport personnel there during regular hours, people just start taking things as soon as the items are unloaded.
Basically, from my experience (I flew from DC to SFO with Cosmo), no airport personnel checks if what people are taking/grabbing are actually theirs! :mad: (it's a mad dash and people are in a hurry.)
So make sure you're there early and get Zumi as soon as you see his crate and that no one takes him/his crate.
Hope this helps!
(P.S. The process may be different if you use a pet "shipping company" and if so, make sure you ask them the detailed step-by-step process of how they do this.
Have you checked Pet Air as another option?)