They obviously have some interest to fly you out, so relax and do the interview and be courteous and all that. But don't worry an iota about their expense: it's part of their budget.
+1. They budget for these things and usually it's one of, if not the last, steps in the hiring process. Almost every time I've flown out for an interview, the offer came soon thereafter. They wouldn't be spending money on you if they didn't think there was a good shot at a fit, so as others have said, RELAX. Be at ease - they obviously are serious enough to spend maybe $1k on getting you out and back (hotel, flight, time with personnel in the office, etc.) so while you may not have it totally in the bag, I'd say if you don't fuck it up, you're almost there :) Just come prepared, know your shit, and you'll do fine!
Premature though it is, CONGRATS ON THE NEW JOB! :)
Seconding this. You'll only be doing yourself a disservice if you're stressed/anxious/tense. Just make sure to sleep and eat well, and maybe iron your clothes if necessary.
Premature though it is, CONGRATS ON THE NEW JOB! :)