Connector for a fluid transport line of a medical device, comprising: a first body having a first access port for a fluid, a second access port for a fluid, and a first fluid path extending in the first body and directly connecting, for fluid transport, the first access port and second access port, at least a second body, mountable to the first body, having at least a third access port for a fluid, the second body being movable with respect to the first body at least between: a main operating position in which the first fluid path is interrupted and in which a second fluid path is defined and enabled, for fluid transport, from the first access port to the third access port, and an auxiliary operating position in which the first fluid path is enabled and in which the second fluid path is interrupted. The second body has at least a fourth access port for a fluid and in the main operating position a third fluid path is defined and enabled, for fluid transport, from the second access port to the fourth access port, the third fluid path being interrupted in the auxiliary operating position.