Kit (10; 90; 100; 120; 160) for treating a blood circulation vessel, of the type comprising: - a valve support which can be deformed radially between a contracted state and a dilated state, the valve support comprising: • at least one external peripheral wall which is intended to press against a wall of the blood circulation vessel, the external peripheral wall delimiting a central passage having a centre axis (X-X'); • an internal peripheral wall which is fixedly joined to the external peripheral wall and which delimits an internal aperture having a radial dimension which is smaller than that of the central passage; and • means for retaining the internal peripheral wall at least partially with radial spacing from the or each external peripheral wall; and - a prosthetic valve which comprises a shutter which can be radially deformed and which is intended to be positioned on the internal peripheral wall in the aperture in order to selectively block the aperture; the retention means and the internal peripheral wall delimiting in a fluid-tight manner, an inner blood circulation region which opens at the proximal and distal ends of the valve support and which contains the aperture, and an external annular region in order to force the blood which flows in the vessel to pass into the inner region through the aperture, the internal peripheral wall extending in the central passage, axially in register with the or each external peripheral wall, characterised in that the retention means comprise a distal peripheral skirt (54; 106) and a proximal peripheral skirt (56; 108) which extend in the space between the internal peripheral wall and the external peripheral wall.. - a valve support which can be deformed radially between a contracted state and a dilated state, the valve support comprising: • at least one external peripheral wall which is intended to press against a wall of the blood circulation vessel, the external peripheral wall delimiting a central passage having a centre axis (X-X'); • an internal peripheral wall which is fixedly joined to the external peripheral wall and which delimits an internal aperture having a radial dimension which is smaller than that of the central passage; and • means for retaining the internal peripheral wall at least partially with radial spacing from the or each external peripheral wall; and • at least one external peripheral wall which is intended to press against a wall of the blood circulation vessel, the external peripheral wall delimiting a central passage having a centre axis (X-X'); • an internal peripheral wall which is fixedly joined to the external peripheral wall and which delimits an internal aperture having a radial dimension which is smaller than that of the central passage; and • means for retaining the internal peripheral wall at least partially with radial spacing from the or each external peripheral wall; and - a prosthetic valve which comprises a shutter which can be radially deformed and which is intended to be positioned on the internal peripheral wall in the aperture in order to selectively block the aperture; the retention means and the internal peripheral wall delimiting in a fluid-tight manner, an inner blood circulation region which opens at the proximal and distal ends of the valve support and which contains the aperture, and an external annular region in order to force the blood which flows in the vessel to pass into the inner region through the aperture,