Amorphous-amorphous transformations under pressure are generally explained by changes in the local structure from low to higher fold coordinated polyhedra [1-4]. However, as the notion of scale invariance at the critical thresholds has not been addressed, it is still unclear whether these transformations could be associated to true phase transitions. Here we report ab initio based calculations of compressed silica (SiO2) glasses showing that the structural changes from low- to high-density amorphous structures occur through a sequence of percolation transitions. When the pressure is increased up to 82 GPa, a series of long range ('infinite') percolating clusters built up by corner- or edge-shared tetrahedra, pentahedra, and eventually octahedra, emerge at some critical pressures and replace the previous phase of lower fold coordinated polyhedra and lower connectivity. This mechanism provides a natural explanation for the well-known mechanical anomaly around 3 GPa as well as for the structural irreversibility beyond 10 GPa, among others. Some of the amorphous structures that have been discovered mimic those of coesite IV and V crystals reported recently [5,6], highlighting the major role of SiO5 pentahedra-based polyamorphs in the densification process of vitreous silica. Our observations demonstrate that the percolation theory provides a robust framework to understand the nature and the pathway of the amorphous-amorphous transformations, and open a new avenue to predict unraveled amorphous solid phases and related liquids [7,8].