Qualitative models of dynamics of signalling pathways and gene regulatory networks allow to capture temporal properties of biological networks while requiring few parameters. However, these discrete models typically suffer from the so-called state space explosion problem which makes the formal assessment of their potential behaviours very challenging. In this paper, we describe a method to reduce a qualitative model for enhancing the tractability of analysis of transient reachability properties. The reduction does not change the dimension of the model, but instead limits its degree of freedom, therefore reducing the set of states and transitions to consider. We rely on a transition-centered specification of qualitative models by the mean of automata networks. Our framework encompass usual asynchronous Boolean and multi-valued network, as well as 1-bounded Petri nets. Applied to different large-scale biological networks from the litterature, we show that the reduction can lead to drastic improvement for the scalability of verification methods.