Regular cash systems provide both the {\em anonymity} of users and the transferability of coins. In this paper, we study the anonymity properties of transferable e-cash. We define two natural additional levels of anonymity directly related to transferability and not reached by existing schemes that we call full anonymity (FA) and perfect anonymity (PA). We show that the FA property can be reached by providing a generic construction and that the PA's cannot. Next, we define two restricted perfect anonymity properties and we prove that it is possible to design a transferable e-cash scheme where a bounded adversary not playing the bank cannot recognize a coin he has already owned.