A conditioning device for conditioning an exposed stretch of a blood vessel has an envelope and at least one conveying channel extending entirely within the envelope. The envelope has a first layer having a first surface facing the exposed stretch, and a second layer having a second surface, opposite to the first surface. The at least one conveying channel has at least one first aperture leading out of the envelope, so that the at least one conveying channel is suppliable with working fluid through the at least one first aperture. The first layer is permeable to at least one component of the working fluid, so that, when the working fluid is in the at least one conveying channel, the at least one component, permeating the first layer, diffuses until reaching the first surface to apply a conditioning action on the exposed stretch of the blood vessel.