To address your original post, there is no chicken wire, Chechen wire, or any other kind of wire or wire mesh used in the 30-31 PU tops.
In a nutshell, here is the procedure:
1. Stretch cotton canvas black duck over your roof ribs and tack in place. The ribs should be painted and are exposed inside the cab. I painted mine gloss black, but I don't know if that's kosher; I just liked the look with the black duck. (The attached photo shows the black duck and interior of my PU.) Black duck can be difficult to find. The stuff I got from LeBaron Bonney was not correct, was too soft, and was not cotton. I sent it back. I finally found some at a local sail maker's shop. And it wasn't cheap.
2. Spread a thin layer of cotton batting (not foam) over the duck, with decreasing amounts down the sides and none by the time you get to the gutter.
3. Stretch your top fabric into place and tack it down. It helps to do this on a warm day after the top material has had time to lay in the sun for a couple hours.
Follow the instructions in the link above for all the nitty gritty of installation and how to trim and how the top fits with the gutters. I don't remember how that is because I couldn't do that with the type of gutters I have. But if you're going for show you'll want to read that section in the link.