Kinetic criteria are formulated describing vitrification and devitrification of liquids in response to variations of the rate of change of external pressure. General analytical relations are derived allowing one to determine the pressure at the glass vansition, p(g), and the width of the glass transition interval, delta p(g), in dependence on the rate of change of pressure. In addition, a direct correlation between the pressure at the glass transition and the width of the glass transition interval is established. It is shown that the ratio delta p(g)/p(g) is determined generally by an appropriately defined fragility index being a measure of the steepness of change of relaxation time at the glass transition, p(g), relevant for the selected rate of change of pressure. Similar relations are derived also for dynamic glass transitions in response to oscillations of pressure. All these dependencies are widely determined by the Maxwellian relaxation time of the liquid under consideration. However, they are shown to hold independently of any particular assumptions concerning the particular type of dependence of viscosity and/or relaxation time on pressure and the set of structural order-parameters describing the effect of deviations from (metastable) thermodynamic equilibrium. The results are illustrated here utilizing a recently developed new relation for the pressure dependence of the Newtonian viscosity, respectively, the relation for the pressure dependence of the relaxation time corresponding to it. Similarly to vitrification caused by variations of temperature, the pressure at the glass transition and the width of the glass transition range are shown to be logarithmic functions of the rate of change of pressure. The analytical results are confirmed by numerical computations employing a simple statistical model of glass-forming liquids.