The practical advantage expected from transferable e-cash compare to non-transferable is the significant reduction of the interaction number between the bank and the users. However, this property is not fulfilled by {\em anonymous} transferable e-cash schemes of the state-of-the art. In this paper, we first present a transferable e-cash scheme with a reduced number of communications between the bank and the users that fulfils the {\em computational anonymity} property. Next, we present a transferable e-cash scheme with a reduced interaction number that fulfils the {\em unconditional anonymity}. This latter scheme is quite less efficient.