Rapidly quenched glass formers are amorphous and transformed into glass phases by relaxing enthalpy during the first heating. Two liquids give rise, at first, to an intermediate Phase 3 below T3 < Tg respecting the entropy constraints and then, the enthalpy increases towards that of the glass phase up to Tg. The negative activation energy shows that Phase 3 is hidden behind the glassy phase acting as an intermediate invasive phase during the second cooling. Phase 3 carries a medium-range order above Tg which can be superheated above the melting temperature up to Tn+. The two-liquid state model predicts the thermodynamic properties as well as the relaxation times from liquids 1 to 2. The configuron model is successfully applied to 54 glasses explaining the transitions by percolation and an ‘ordered’ fraction equal to the critical threshold Φc = 0.15 ± 0.01 from Tg to Tn+.