In this assembly; each connecting piece comprises engaging means situated outside said conduit for engaging a connecting bar and outside said conduit for engaging on an anchor member, making it possible to grasp said connecting piece using a handling instrument. The assembly comprises at least one handling instrument comprising engaging means complementary to those comprised by each connecting piece. According to the invention, each anchor member is equipped with a proximal shaft, the length of which is such that it protrudes past the patient's skin after implantation of said anchor member on a vertebra. Each handling instrument is tubular and can be engaged on the proximal shaft of each anchor member so as to allow the movement of a connecting piece grasped by the instrument along the proximal shaft of each anchor member.