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

We consider here an interacting dark matter-dark energy model with a non-zero spatial curvature component and a freely varying dark energy equation of statein both the quintessential and phantom regimes.A phantom and closed universe can perfectly alleviate the hubble tension, without the necessity of a coupling among the dark sectors.Accounting for other possible cosmological observations compromises the viability of this very attractive scenario as a global solutionto current cosmological tensions, either by spoiling its effectivenessconcerning the problem, as in the case of supernovae ia data, or by introducing a strong disagreement in the preferred value of the spatialcurvature, as in the case of baryon acoustic oscillations.