Water is unique in many ways. One of the most remarkable peculiarities of water is its polyamorphism, i.e., its capability to acquire more than one amorphous state. The very nature of amorphous ices is still highly debated, but even less is known about their connection to the liquid state. The possibility of a continuous thermodynamic link between the supercooled liquid(s) and the amorphous ices is highly debated. On the other hand, probing such connection is a challenging task, mostly because of the lack of theoretical and/or experimental tools able to account for the high degeneracy of local configurations in statistically isotropic materials. In this work, we bypass these difficulties by proposing a new strategy that explores structural similarity between the different disordered configurations. We combine GPU-accelerated molecular dynamics simulations with a neural network approach that allows us to clarify the connections between equilibrium liquid water and its amorphous/glass states. Moreover, our results also confirm that liquid water can be interpreted as a two state system, an hypothesis that was always considered at the theoretical level and that is at the heart of water anomalies.