  We study the low temperature out of equilibrium Monte Carlo dynamics of the
disordered Ising $p$-spin Model with $p=3$ and a small number of spin
variables. We focus on sequences of configurations that are stable against
single spin flips obtained by instantaneous gradient descent from persistent
ones. We analyze the statistics of energy gaps, energy barriers and trapping
times on sub-sequences such that the overlap between consecutive configurations
does not overcome a threshold. We compare our results to the predictions of
various trap models finding the best agreement with the step model when the
$p$-spin configurations are constrained to be uncorrelated.
