  The description of activated relaxation of glassy systems in the
multidimensional configurational space is a long-standing open problem. We
develop a phenomenological description of the out-of-equilibrium dynamics of a
model with a rough potential energy landscape and we analyse it both
numerically and analytically. The model provides an example of dynamics where
typical relaxation channels go over finite potential energy barriers despite
the presence of less-energy-demanding escaping paths in configurational space;
we expect this phenomenon to be also relevant in the thermally activated regime
of realistic models of glass-formers. In this case, we found that typical
dynamical paths episodically reach an high fixed threshold energy unexpectedly
giving rise to a simple thermally activated aging phenomenology. In order to
unveil this peculiar aging behavior we introduce a novel description of the
dynamics in terms of spontaneously emerging dynamical basins.
