A connection device for assembling together a receiver first section member presenting an inner cavity, and a fastener second section member presenting a groove having a constricted opening. The connection device includes a cage forming a pair of jaws for coming into engagement in the groove. The device also including a resilient drive mechanism for urging a spacer member between the jaws so as to space them apart in such a manner as to come into engagement with the groove through the constricted opening; and a pivotable lever that pivots about a pivot pin, the pivotable lever including a lever arm and a thrust head that engages the spacer member so as to move it against the force exerted by the resilient drive mechanism on the spacer member.