Water exists in at least two families of glassy states, broadly categorized as the low-density (LDA) and high-density amorphous ice (HDA). Remarkably, LDA and HDA can be reversibly interconverted via appropriate thermodynamic paths, such as isothermal compression and isobaric heating, exhibiting first-order-like phase transitions. We perform out-of-equilibrium molecular dynamics simulations of glassy water using the ST2 model to study the evolution of LDA and HDA upon isobaric heating. Depending on pressure, glass-to-glass, glass-to-crystal, glass-to-vapor, as well as glass-to-liquid transformations are found. Specifically, heating LDA results in the following transformations, with increasing heating pressures: (i) LDA-to-vapor (sublimation), (ii) LDA-to-liquid (glass transition), (iii) LDA-to-HDA-to-liquid, (iv) LDA-to-HDA-to-liquid-to-crystal, and (v) LDAto-HDA-to-crystal. Similarly, heating HDA results in the following transformations, with decreasing heating pressures: (a) HDA-to-crystal, (b) HDA-to-liquid-to-crystal, (c) HDA-to-liquid (glass transition), (d) HDA-to-LDA-to-liquid, and (e) HDA-to-LDA-to-vapor. A more complex sequence may be possible using lower heating rates. For each of these transformations, we determine the corresponding transformation temperature as function of pressure, and provide a P-T "phase diagram" for glassy water based on isobaric heating. Our results for isobaric heating dovetail with the LDA-HDA transformations reported for ST2 glassy water based on isothermal compression/decompression processes [Chiu et al., J. Chem. Phys. 139, 184504 (2013)]. The resulting phase diagram is consistent with the liquid-liquid phase transition hypothesis. At the same time, the glass phase diagram is sensitive to sample preparation, such as heating or compression rates. Interestingly, at least for the rates explored, our results suggest that the LDA-to-liquid (HDA-to-liquid) and LDA-to-HDA (HDA-to-LDA) transformation lines on heating are related, both being associated with the limit of kinetic stability of LDA (HDA).