By "reversible" do you mean the ability to reverse the direction by locking the chuck to the spindle? If so, all the Nova chucks that is inserts have set screws to lock the insert to the chuck body. Most of the inserts come drilled and tapped to lock the insert to the spindle and so locking the chuck to the spindle. But check - some of the inserts do not come with the locking screw capability although it could be added.
I'm quite satisfied with Nova chucks. I use 1-1/4" x 8 inserts on all of them (except for one I save for the Jet mini lathes). I use 4 types of Nova chucks but I prefer the Supernova 2, mostly because of the hex chuck key. However, I buy used Supernova chucks of the price is right and have some G3 chucks when on sale. All are capable chucks.
JKJ