A cover including an elongate body, capable of being applied to be facing an outer surface of the pipe, and at least one longitudinal interaction element for interacting with the pipe, supported by the elongate body. The elongate body is reversibly deformable under the effect of its own weight, the elongate body having a length of more than 10 m. The cover treats solid build-ups within a fluid-transport pipe in a simple, straightforward and inexpensive manner.