One of the things I miss most about living in AZ is the common sense when it comes to these things. Both in the written law and the application. Either way, as long as you are not waving it around and threatening people, and/or they don't find it sticking out of someone, they are pretty much not going to care.
AZ passed the concealed carry after I left, so I imagine it's even easier. The exceptions were banks, courthouses, bars, and any facility that has posted a "no guns" or "no weapons" sign. (Again, common sense) I think it's safe to assume you still shouldn't carry there.
I lived out in the open desert, and carried a nice .45LC Remington m. 1895 and a handmade coffin handled Bowie with a 10' blade. Never had anyone even ask me about it other than to "talk shop" and compare to theirs, including the cops
A lot of California Libs have been moving to Phoenix and Tucson lately, so things may change, and you are much more likely to run into someone wanting to cause trouble for you there, so I would recommend to err on the side of caution when traveling around there. I generally didn't open carry in those areas due to the political types, and most businesses in Phx had posted signs anyway. There may be City Ordinances to worry about as well.
Also, the cops in Mesa, at least when I was there, have a real attitude problem so be careful around them in any regard.
Unless they have changed it, switchblades were legal, but butterfly knives were not, which is the only law that made no sense to me.