  We analyze the properties of the energy landscape of {\it finite-size} fully
connected $p$-spin-like models. In the thermodynamic limit the high temperature
phase is described by the schematic Mode Coupling Theory of super-cooled
liquids. In this limit the barriers between different basins are infinite below
the critical dynamical temperature the ergodicity is broken on in infinite
times. We show that {\it finite-size} fully connected $p$-spin-like models,
where activated processes are possible, do exhibit properties typical of real
super-cooled liquid when both are near the critical glass transition. Our
results support the conclusion that fully-connected $p$-spin-like models are
the natural statistical mechanical models for studying the glass transition in
super-cooled liquids.
