A transfer set for transferring fluid, including drugs, vaccines, medicaments, solutions and the like, between a first container, such as a conventional vial, and a second container, such as a conventional syringe having a unique multipurpose resealable member. The transfer set assembly includes an elastomeric tubular fluid transfer and resealable valve member preferably including an open end mounted on the pierceable closure or stopper of a vial and a generally closed distal end having a longitudinal slit and a piercing member is telescopically received within the fluid transfer valve member having a piercing end opposite the pierceable closure. The fluid transfer valve member is preferably formed of silicone and is surrounded by a generally tubular luer connector member having an open end mounted on the pierceable closure and a distal end having male luer threads. This assembly is enclosed within a cup-shaped closure and the assembly is retained to the first container or vial by a collar preferably secured to the vial by crimping. Upon removal of the cup-shaped closure, fluid communication between the vial and a second container, such as a syringe, is achieved by threading the luer connector of the syringe on the luer threads of the tubular luer connector member, which drives the tip through the slit of the elastomeric fluid transfer valve member against the distal end of the piercing member, driving the piercing end through the pierceable closure. In the preferred embodiment, the piercing member includes a generally longitudinal channel which establishes communication between the vial and the syringe through the tubular fluid transfer valve member.