Dense-Time Petri nets (TPNs) are an extension of Petri nets where each transition has its own clock and time interval. This model is considered in the context of a weak semantics, in which time elapsing does not force transitions to fire. For TPNs, equivalences are investigated in the dichotomies of "interleaving — partial order" and "linear — branching time". The relationships between equivalences are analyzed with respect to intermediate and persistent atomic memory policies, which determine the rules for resetting the clocks of transitions.