An understanding of water's anomalies is closely linked to an understanding of the phase diagram of water's metastable noncrystalline states. Despite the considerable effort, such an understanding has remained elusive and many puzzles regarding phase transitions in supercooled liquid water and their possible amorphous proxies at low temperatures remain. Here, decompression of very high density amorphous ice (VHDA) from 1.1 to 0.02 GPa at 140 K is studied by means of dilatometry and powder x-ray diffraction of quench-recovered states. It is shown that the three amorphous states of ice are reversibly connected to each other, i.e., LDA<-->e-HDA<-->VHDA. However, while the downstroke VHDA-->e-HDA transition takes place in the pressure range of 0.06 GPa<p<0.40 GPa, the e-HDA-->LDA transition takes place quasi-discontinuously at p approximately 0.06 GPa. That is, two amorphous-amorphous transitions of a distinct nature are observed for the first time in a one-component system-a first-order-like transition (e-HDA-->LDA) and a transition which is not first-order like but possibly of higher order (VHDA-->e-HDA). VHDA and e-HDA are established as the most stable and limiting states in the course of the transition. We interpret this as evidence disfavoring the hypothesis of multiple first-order liquid-liquid transitions (and the option of a third critical point), but favoring a single first-order liquid-liquid transition (and the option of a second critical point).