Connecting part for biopharmacy, capable of connecting a first container or conduit and a second container or conduit for the transfer of a certain biopharmaceutical product from the first container or conduit to the second container or conduit, forming a whole: ▪ A connecting sheath closed laterally on itself, provided at its first free end part and at its second free end part with a first communication opening and a second communication opening, capable of forming and limiting an inner connecting space, a free end edge delimiting the first communication opening and another free end edge delimiting the second communication opening, ▪ At the first free end part, a first annular and peripheral outer connecting skirt, whose inner lateral face is capable of coming into contact with elastic tightening for holding and sealing on a part mated to the outer face of a first collar, ▪ At the second free end part, a second annular and peripheral outer connecting skirt, whose inner lateral face is capable of coming into contact with elastic tightening for holding and sealing on a part mated to the outer face of a second collar, ▪ The sheath and the skirts (38a, 38b) being integral, made of an inherently airtight material for biopharmacy and having an elasticity such that the connecting part is capable of being stretched transversely at the site of its two skirts (38a, 38b) and, by its elasticity, coming into contact with elastic tightening for holding and sealing on the part mated to the outer face of the collars (14, 24), without the necessity for an extrinsic attachment part, ▪ The connecting part being capable of, in the assembled state with the first container or conduit and the second container or conduit and in a communication configuration, allowing transfer of the biopharmaceutical product from the first container or conduit to the second container or conduit, characterized by the fact that: ▪ The inner face of the connecting part is essentially without rough spots, reliefs or roughness so as not to slow down the transfer of biopharmaceutical product and not to keep the product inside the connecting part, ▪ The connecting sheath has, in the assembled state and in a communication configuration, a general cylindrical or tapered shape with a transverse cross-section that is at least approximately circular or pseudo-circular, ▪ The inner lateral faces of one and the other of the skirts (38a, 38b) comprises, successively with increasing proximity to a corresponding free end edge, a cylindrical zone of larger inside diameter adjacent to the sheath, a tapering zone and a cylindrical zone of smaller inside diameter adjacent to the free end edge (32a, 32b) of the connecting part, the tapered zone being placed between the cylindrical zone of larger inside diameter and the cylindrical zone of smaller inside diameter, extending between these two cylindrical zones of the skirt (38a, 38b). ▪ A connecting sheath closed laterally on itself, provided at its first free end part and at its second free end part with a first communication opening and a second communication opening, capable of forming and limiting an inner connecting space, a free end edge delimiting the first communication opening and another free end edge delimiting the second communication opening, ▪ At the first free end part, a first annular and peripheral outer connecting skirt, whose inner lateral face is capable of coming into contact with elastic tightening for holding and sealing on a part mated to the outer face of a first collar, ▪ At the second free end part, a second annular and peripheral outer connecting skirt, whose inner lateral face is capable of coming into contact with elastic tightening for holding and sealing on a part mated to the outer face of a second collar, ▪ The sheath and the skirts (38a, 38b) being integral, made of an inherently airtight material for biopharmacy and having an elasticity such that the connecting part is capable of being stretched transversely at the site of its two skirts (38a, 38b) and, by its elasticity, coming into contact with elastic tightening for holding and sealing on the part mated to the outer face of the collars (14, 24), without the necessity for an extrinsic attachment part, ▪ The connecting part being capable of, in the assembled state with the first container or conduit and the second container or conduit and in a communication configuration, allowing transfer of the biopharmaceutical product from the first container or conduit to the second container or conduit, ▪ The inner face of the connecting part is essentially without rough spots, reliefs or roughness so as not to slow down the transfer of biopharmaceutical product and not to keep the product inside the connecting part, ▪ The connecting sheath has, in the assembled state and in a communication configuration, a general cylindrical or tapered shape with a transverse cross-section that is at least approximately circular or pseudo-circular, ▪ The inner lateral faces of one and the other of the skirts (38a, 38b) comprises, successively with increasing proximity to a corresponding free end edge, a cylindrical zone of larger inside diameter adjacent to the sheath, a tapering zone and a cylindrical zone of smaller inside diameter adjacent to the free end edge (32a, 32b) of the connecting part, the tapered zone being placed between the cylindrical zone of larger inside diameter and the cylindrical zone of smaller inside diameter, extending between these two cylindrical zones of the skirt (38a, 38b).