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We aim to combine asteroseismology, spectroscopy, and evolutionary models toestablish a comprehensive picture of the evolution of Galactic blue supergiantstars (BSG). To start such an investigation, we selected three BSG candidatesfor our analysis: HD 42087 (PU Gem), HD 52089 ($\epsilon$ CMa) and HD 58350($\eta$ CMa). These stars show pulsations and were suspected to be in anevolutionary stage either preceding or succeding the red supergiant (RSG)stage.  For our analysis, we utilized the 2-min cadence TESS data to study thephotometric variability and obtained new spectroscopic observations at theCASLEO observatory. We calculated CMFGEN non-LTE radiative transfer models andderived stellar and wind parameters using the iterative spectral analysispipeline XTGRID. The spectral modeling was limited to changing only theeffective temperature, surface gravity, CNO abundances, and mass-loss rates.Finally, we compared the derived metal abundances with predictions from Genevastellar evolution models. The frequency spectra of all three stars show eitherstochastic oscillations, nonradial strange modes, or a rotational splitting.  We conclude that the rather short sectoral observing windows of TESS preventestablishing a reliable mode identification of low frequencies connected tomass-loss variabilities. The spectral analysis confirmed gradual changes in themass-loss rates and the derived CNO abundances comply with the values reportedin the literature. We were able to achieve a quantitative match with stellarevolution models for the stellar masses and luminosities. However, thespectroscopic surface abundances turned out to be inconsistent with theoreticalpredictions. The stars show N enrichment, typical for CNO cycle processedmaterial, but the abundance ratios do not reflect the associated levels of Cand O depletion.

Unveiling the evolutionary state of three B supergiant stars: PU Gem, $\epsilon$ CMa and $\eta$ CMa