  We aim to combine asteroseismology, spectroscopy, and evolutionary models to
establish a comprehensive picture of the evolution of Galactic blue supergiant
stars (BSG). To start such an investigation, we selected three BSG candidates
for 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 an
evolutionary stage either preceding or succeding the red supergiant (RSG)
stage.
  For our analysis, we utilized the 2-min cadence TESS data to study the
photometric variability and obtained new spectroscopic observations at the
CASLEO observatory. We calculated CMFGEN non-LTE radiative transfer models and
derived stellar and wind parameters using the iterative spectral analysis
pipeline XTGRID. The spectral modeling was limited to changing only the
effective temperature, surface gravity, CNO abundances, and mass-loss rates.
Finally, we compared the derived metal abundances with predictions from Geneva
stellar evolution models. The frequency spectra of all three stars show either
stochastic oscillations, nonradial strange modes, or a rotational splitting.
  We conclude that the rather short sectoral observing windows of TESS prevent
establishing a reliable mode identification of low frequencies connected to
mass-loss variabilities. The spectral analysis confirmed gradual changes in the
mass-loss rates and the derived CNO abundances comply with the values reported
in the literature. We were able to achieve a quantitative match with stellar
evolution models for the stellar masses and luminosities. However, the
spectroscopic surface abundances turned out to be inconsistent with theoretical
predictions. The stars show N enrichment, typical for CNO cycle processed
material, but the abundance ratios do not reflect the associated levels of C
and O depletion.
