The connection between phase transitions (PTS) and calorimetric glass transitions (CGTS) is considered, first with reference to second order PTS as described by Ehrenfest, then by comparison with a rheological approach. This results in connecting the partition functions of the 'ideal' liquid with that of the 'ideal' glass, by means of a 'real' partition function, explicitly depending on the cooling (heating) rate. By requiring the entropy and heat capacity at any cooling rate in the rheological model to be positive, it turns out that the CGT sharpens with decreasing difference between the two ideal free energies, and not simply with decreasing cooling rate. In addition, it is impossible to make the two ideal free energies join at arbitrary low cooling rates without singularities, if their difference is non-vanishing at zero temperature. If this is not the case, a lower limiting critical cooling rate is predicted, at which a secondary (or beta ) relaxation toward the glass becomes a true PT. Under special conditions, the primary (or alpha ) relaxation can simulate a true PT, in which case one may speak of a 'false' PT. A classification of glass-forming materials is possible, based on the difference between false PTS simulating first-order PTS (class (A) materials), or second-order PTS (class (B) materials). The rheological model is also discussed in connection with the mode-coupling theory of the glass transition.