Welcome to the forum mintaka. If I understand your post correctly you're a former NY resident curious about carry in AZ in general?
Basically, anyone over the age of 18 can open carry without a permit, end of story. Until July 29 of this year, you can CCW with a permit and after that date, you can CCW with out a permit. If you weapon is accidentally exposed there's no problem, at least not legally. Tactically it's another story.
For more information, read up on the Arizona Revised Statutes Title 13, specifically 13-3112, and read the Arizona page at www.handgunlaw.us