As shown by early studies on mean-field models of the glass transition, the geometrical features of the energy landscape provide fundamental information on the dynamical transition at the Mode-Coupling temperature $T_d$. We show that active particles can serve as a useful tool for gaining insight into the topological crossover in model glass-formers. In such systems the landmark of the minima-to-saddle transition in the potential energy landscape, taking place in the proximity of $T_d$, is the critical slowing down of dynamics. Nevertheless, the critical slowing down is a bottleneck for numerical simulations and the possibility to take advantage of the new smart algorithms capable to thermalize down in the glass phase is attractive. Our proposal is to consider configurations equilibrated below the threshold and study their dynamics in the presence of a small amount of self-propulsion. As exemplified here from the study of the p-spin model, the presence of self-propulsion gives rise to critical off-equilibrium equal-time correlations at the minima-to-saddles crossover, correlations which are not hindered by the sluggish glassy dynamics.
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