This equipment includes at least one U-shaped clip (1) whose lateral branches (10) have sections and widths such that they may be inserted in the vertebral bodies (100) of two vertebrae by impaction on the intermediate branch (11) of the clip (1), so as to rest along the cortical bones of the vertebral bodies, and whose intermediate branch (11) is deformable in such a way as to allow a reduction of the distance between the lateral branches (10); the intermediate branch, before implantation, has a length such that one of the lateral branches (10) may be positioned slightly above the cortical bone forming the plate of the subjacent vertebra while the other lateral branch (10) may be positioned slightly below the cortical bone forming the plate of the subjacent vertebra, and has, after deformation, a length such that the two lateral branches (10) may be brought closer to each other.