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

Testing the consistency between cosmological data: the impact of spatial curvature and the dark energy EoS