First, we cut off the bottoms of the zips, right in between the last tooth and the end stop. We usually use a tool called Erdi Snips, but Cutco Shears also work great. Even regular scissors work as well (though with a little bit of gnawing.)
Fray Block is then applied to seal the raw edges; Fray-Check is also fine to use instead. This is a very important step, to make sure the threads don't unravel. (The below photo shows the right side segment in two pieces - please disregard...at this stage, both sides to be connected should remain in the zipped position.)
Then, instead of just throwing away the ends, they actually will factor back into the connecting process. Since the thick polyester zipper tape has a thick grain to it, that means it has a great grip - especially if being stuck to itself. After cutting the bottoms of the now-useless endstop (which -does- get tossed), they are cut into the following funny tab-shape.
Fray Block / Check is also applied to the edges of the "join strips" so they don't unravel either.
The unusual shape of the join strips is important because the little tab must fit in between two teeth perfectly to join the zippers - rather like floss on real teeth. The last teeth from both cut-up zips can be fed right into each other, with the join strip to be placed on top of them.
We -used- to use Weld-it on the tabs here, but after doing this for a while, we have found that The Amazing Goop, though thicker, is much more effective and will have the splices be much more durable - though you'll need a small stick to get it in between the teeth of the zipper. After coating both the entire tab and the zipper tape where the tab will be placed (and letting them dry for five minutes) the pieces are then stuck together firmly. Forceps can hold the tabs down in between the teeth as it sets up overnight, though this isn't that necessary with Goop as it had been with Weld-it. This is repeated on the reverse side, directly underneath, making a little sandwich of zipper tape over the cut line.
As you can see, it's hard to tell where the tabs are glued in, even when looking at the light grey zips for better contrast here. (This is, of course, ideal, though annoying for illustrative purposes.)