Zips and Zippers

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I'm currently reading Differential Manifolds by Antoni Kosinski, and the concept of a zip--defined as half of a zipper--is mentioned early on, of course with the intent of connecting manifolds. This seems very geometrically intuitive, but I cannot find a general, mathematical definition of a zip or a zipper. Would these geometric ideas be shown mathematically as the different methods which one can connect manifolds with, or does there exist a general definition?