I have never heard of an "AAV" for a toilet. How does it work and where would it be located? The only alternate vents I have installed were for kitchen sinks...you know those under the counter jobs.
I would never use one on a toilet for a couple of reasons. You'd either have to have it exposed, or in the wall. Leaving it under the floor is kinda silly, since you SHOULD be running it above the flood rim. If it gets stuck open and sewer backs up, its going to come out of there before the toilet overflows.
If it's exposed, it's going to be ugly. If it's in the wall, there's a chance that a spider is going to crawl into there and get it stuck open. Then you have sewer gas escaping into your wall, and that = demo. to fix it.