Glassy water occurs in at least two broad categories: low-density amorphous (LDA) and highdensity amorphous (HDA) solid water. We perform out-of-equilibrium molecular dynamics simulations to study the transformations of glassy water using the ST2 model. Specifically, we study the known (i) compression-induced LDA-to-HDA, (ii) decompression-induced HDA-to-LDA, and (iii) compression-induced hexagonal ice-to-HDA transformations. We study each transformation for a broad range of compression/decompression temperatures, enabling us to construct a "P-T phase diagram" for glassy water. The resulting phase diagram shows the same qualitative features reported from experiments. While many simulations have probed the liquid-state phase behavior, comparatively little work has examined the transitions of glassy water. We examine how the glass transformations relate to the (first-order) liquid-liquid phase transition previously reported for this model. Specifically, our results support the hypothesis that the liquid-liquid spinodal lines, between a lowdensity and high-density liquid, are extensions of the LDA-HDA transformation lines in the limit of slow compression. Extending decompression runs to negative pressures, we locate the sublimation lines for both LDA and hyperquenched glassy water (HGW), and find that HGW is relatively more stable to the vapor. Additionally, we observe spontaneous crystallization of HDA at high pressure to ice VII. Experiments have also seen crystallization of HDA, but to ice XII. Finally, we contrast the structure of LDA and HDA for the ST2 model with experiments. We find that while the radial distribution functions (RDFs) of LDA are similar to those observed in experiments, considerable differences exist between the HDA RDFs of ST2 water and experiment. The differences in HDA structure, as well as the formation of ice VII (a tetrahedral crystal), are a consequence of ST2 overemphasizing the tetrahedral character of water. © 2013 AIP Publishing LLC.