In this paper we study the model of Time Potri Nets (TPNs) where a time interval is associated with the firing of a transition, but we extend it by considering general intervals rather than closed ones. A key feature of timed models is the memory policy, i.e. which timing informations are kept when a transition is fired. The original model selects an intermediate semantics where the transitions disabled after consuming the tokens, as well as the firing transition, are reinitialised. However this semantics is not appropriate for some applications. So we consider here two alternative semantics: the atomic and the persistent atomic ones. First we present relevant patterns of discrete event systems which show the interest of these semantics. Then we compare the expressiveness of the three semantics w.r.t. weak timed bisirnilarity, establishing inclusion results in the general case. Furthermore we show that some inclusions are strict with unrestricted intervals even when nets are bounded. Then we focus on bounded TPNs with upper-closed intervals arid we prove that the semantics are equivalent. Finally taking into account both the practical and the theoretical issues, we conclude that persistent, atomic semantics should be preferred.