  Cell monolayers and epithelial tissues display slow dynamics during the
liquid-glass transitions, a phenomenon with direct relevance to embryogenesis,
tumor metastases, and wound healing. In active cells, persistent motion and
cell deformation compete, significantly influencing relaxation dynamics. Here,
we numerically construct the liquid-glass transition phase diagram for
two-dimensional polydisperse persistent cells. We employ cage-relative measures
and conduct extensive simulations to eliminate the influence of system size
effects. These effects arise from long-wavelength fluctuations in nearly
equilibrated cells and a combination of long-wavelength fluctuations and
non-equilibrium effects in highly persistent cells. Our study unveils
distinctive intermittent dynamics associated with intermittent T1 transitions
in highly persistent cells, where the velocity correlates over space with a
characteristic length $\xi$. The $\alpha$ relaxation time exhibits a universal
power-law dependence on the irreversible T1 transition rate,
$\Gamma_{\rm{T1}}^{\rm irr}$, multiplied by ${\rm exp}(\xi)$. Here, $\xi$
vanishes in nearly equilibrated cells, and $\Gamma_{\rm{T1}}^{\rm irr}$
diminishes towards the mode-coupling glass transition point.
