  We act on the suggestion that an excitonic insulator state might
separate---at very low temperatures---a semimetal from a semiconductor and ask
for the nature of these transitions. Based on the analysis of electron-hole
pairing in the extended Falicov-Kimball model, we show that tuning the Coulomb
attraction between both species, a continuous crossover between a BCS-like
transition of Cooper-type pairs and a Bose-Einstein condensation of preformed
tightly-bound excitons might be achieved in a solid-state system. The precursor
of this crossover in the normal state might cause the transport anomalies
observed in several strongly correlated mixed-valence compounds.
