We present direct evidence of low frequency, radially sheared, turbulence-driven flows (zonal flows (ZFs)) triggering edge transport barrier formation preceding the L- to H-mode transition via periodic turbulence suppression in limit-cycle oscillations (LCOs), consistent with predator-prey dynamics. The final transition to edge-localized mode-free H-mode occurs after the equilibrium E × B flow shear increases due to ion pressure profile evolution. ZFs are also observed to initiate formation of an electron internal transport barrier (ITB) at the q = 2 rational surface via local suppression of electron-scale turbulence. Multi-channel Doppler backscattering (DBS) has revealed the radial structure of the ZF-induced shear layer and the E × B shearing rate, ωE×B, in both barrier types. During edge barrier formation, the shearing rate lags the turbulence envelope during the LCO by 90°, transitioning to anti-correlation (180°) when the equilibrium shear dominates the turbulence-driven flow shear due to the increasing edge pressure gradient. The time-dependent flow shear and the turbulence envelope are anti-correlated (180° out of phase) in the electron ITB. LCOs with time-reversed evolution dynamics (transitioning from an equilibrium-flow dominated to a ZF-dominated state) have also been observed during the H-L back-transition and are potentially of interest for controlled ramp-down of the plasma stored energy and pressure (normalized to the poloidal magnetic field) in ITER.