  We used 5487 star-forming galaxies at redshift z~0.63 extracted from the
VIPERS and 143774 comparison galaxies in the local Universe from the GSWLC
catalog. We employed two families of methods: parametric and non-parametric. In
the former approaches, we compared the FMR projections plagued by observational
biases on differently constructed control samples at various redshifts. Then,
the metallicity difference between different redshifts in M*-SFR bins. In the
latter approach, we related the metallicity and the normalized sSFR. The
methodologies implemented to construct fair, complete samples for studying the
MZR and the FMR produced consistent results showing a small, but still
statistically significant evolution of both relations up to z~0.63. In
particular, we observed a systematic trend where the median metallicity of the
sample at z=0.63 is lower than that of the local sample at the same M* and SFR.
The average difference in the metallicity of the low and intermediate redshifts
is approximately 1.8 times the metallicity standard deviation of the median, of
the intermediate redshift sample, in M*-SFR bins. We confirmed this result
using the Kolmogorov-Smirnov test. When we applied the M*-completeness
criterion to catalogs, the metallicity difference in redshifts decreased to
approximately 0.96 times the metallicity standard deviation of the median, thus
not statistically significant. This result may be dominated by the limited
parameter space, being the lower M* galaxies where the difference is larger out
from the analysis. A careful reading of the results, and their underlying
selection criteria, are crucial in studies of the mass-metallicity and FMRs.
