  The results of joint analyses of available cosmological data have motivated
an important debate about a possible detection of a non-zero spatial curvature.
If confirmed, such a result would imply a change in our present understanding
of cosmic evolution with important theoretical and observational consequences.
In this paper we discuss the legitimacy of carrying out joint analyses with the
currently available data sets and explore their implications for a non-flat
universe and extensions of the standard cosmological model. We use a robust
tension estimator to perform a quantitative analysis of the physical
consistency between the latest data of Cosmic Microwave Background, type Ia
supernovae, Baryonic Acoustic Oscillations and Cosmic Chronometers. We consider
the flat and non-flat cases of the $\Lambda$CDM cosmology and of two dark
energy models with a constant and varying dark energy EoS parameter. The
present study allows us to better understand if possible inconsistencies
between these data sets are significant enough to make the results of their
joint analyses misleading, as well as the actual dependence of such results
with the spatial curvature and dark energy parameterizations.
