We revisit the epoch of cosmic speed-up characterized by the redshift of transition from a decelerated to an accelerated phase. This redshift is termed the transition redshift (zt). We use the spatially flat and non-flat variants of the most common ΛCDM and XCDM models to put constraints on the transition redshift along with the other model parameters. The data for this analysis come from the recent and updated Pantheon+ supernova (SN) data set and the Hubble parameter measurements obtained from Cosmic Chronometers. We consider both data sets with their respective covariance matrices incorporating all statistical and systematic uncertainties. We observe that using the combined data sets of H(z) and SNe, the best fit value of transition redshift lies in the range 0.61 < zt < 0.79 for all four dark energy models. Incidentally, we observe a positive curvature for the non-flat models, correlations between several model parameters and a strong degeneracy between the curvature and the equation of state parameter.