Abstract: A kit includes: a sleeve (11); a tubular core (12) for stretching the sleeve, tightly covered by the sleeve and adapted to receive internally an elongate member (30); and a thin and flexible sliding element disposed between the sleeve and the core to enable the core to slide relative to the sleeve, which sliding element makes a half-turn over a first end (17) of the core so as thereafter to be disposed inside the core in order to be able to be pulled from the second end (18) of the core; wherein the sliding element includes a net (13) formed of flexible filaments (21, 23) with at least one layer (22) of filaments (23) connected to each other in a predetermined arrangement, which filaments are adapted to slide on the outside surface of the core and to turn back on themselves around the first end of the core.