Run a zig-zag stitch along the edges of the slits. Or, if you really want to keep it stable, use a buttonhole technique to make a buttonhole just wide enough for the elastic (example, if your elastic strips are 1" wide, make a 1" wide buttonhole) and THEN slit it. Some machines have a one-step buttonhole but some don't, so use whatever you have available to you. If you don't have anything, hand-stitch around the edges of the slit. There are probably tutorials around for hand-stitched buttonhole or eyelet techniques, which is what you would need to do.
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