Yes Arizona,but we do not have a waiting period per say. You can walk in and walk out with a gun. Arizona has a 20 day hold on guns bought by a dealer before it can leave the shop.
I can buy a gun the minute it is bought by the dealer but can not pick it up until 20 after the dealer bought it. I can buy a gun on the 17th day for example and will need to wait 3 days.
The reason is to allows police the ability to possibly find one of your guns that may have been stolen, before it might be resold.