People do it all day long when hunting, but be very careful if you plan to do it in an urban area.
You should be ready and willing to be hassled and/or arrested by the police. Practice keeping your hands away from the gun and carefully follow the commands of the police when they confront you. edit: keep it on a sling and do not touch it with your hands would likely build your best case for not brandishing.
That said, any gun that is legally owned may be carried openly in arizona. holding it in your hands may be considered brandishing by the police as holding a gun can be easily construed to be threatening.
I am not a lawyer, this is not legal advice. good luck.