The activation-relaxation technique (ART), a saddle-point search method, is applied to determine the potential energy landscape around supercooled and glassy configurations of a three-dimensional binary Lennard-Jones system. We show a strong relation between the distribution of activation energies around a given glassy configuration and its history, in particular, the cooling rate used to produce the glass and whether or not the glass was plastically deformed prior to sampling. We also compare the thermally activated transitions found by ART around a supercooled configuration with the succession of transitions undergone by the same supercooled liquid during a time trajectory simulated by molecular dynamics. We find that ART is biased towards more heterogeneous transitions with higher activation energies and more broken bonds than the MD simulation.