We examine the mechanisms governing the relaxation process in deeply supercooled liquids, and show that it results from the accumulation local rearrangements that are akin to solid-solid transformations. These events generate long-ranged and anisotropic stresses in the surrounding medium and must be characterized using tensorial observables. We construct an analytical framework to probe their correlations using local stress data and thus demonstrate that events are power-law correlated in space, with a time-dependent amplitude which peaks at the alpha relaxation time tau_alpha. This effect, which becomes stronger near the glass transition, results from the increasingly important role of local stress fluctuations in facilitating relaxation events. Our finding precludes the existence of any length scale beyond which the relaxation process decorrelates.