We consider here Time Petri nets (TPN model). We first propose an abstraction to its generally infinite state space which preserves linear properties1 of the TPN model. Comparing with TPN abstractions proposed in the literature, our abstraction produces graphs which are both smaller and faster to compute. In addition, our characterization of abstracted states allows a significative gain in space. Afterwards, we show how to apply Yoneda?s partial order reduction technique to construct directly reduced graphs useful to verify LTL-X properties of the model. Using our approach, both time and space complexities are significantly reduced.