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Up-to-date cosmological data analyses have shown that \textit{(a)} a closeduniverse is preferred by the Planck data at more than $99\%$ CL, and\textit{(b)} interacting scenarios offer a very compelling solution to theHubble constant tension. In light of these two recent appealing scenarios, weconsider here an interacting dark matter-dark energy model with a non-zerospatial curvature component and a freely varying dark energy equation of statein both the quintessential and phantom regimes. When considering CosmicMicrowave Background data only, a phantom and closed universe can perfectlyalleviate the Hubble tension, without the necessity of a coupling among thedark sectors. Accounting for other possible cosmological observationscompromises the viability of this very attractive scenario as a global solutionto current cosmological tensions, either by spoiling its effectivenessconcerning the $H_0$ problem, as in the case of Supernovae Ia data, or byintroducing a strong disagreement in the preferred value of the spatialcurvature, as in the case of Baryon Acoustic Oscillations.

2021-$H_0$ Odyssey: Closed, Phantom and Interacting Dark Energy Cosmologies