2021-$H_0$ Odyssey: Closed, Phantom and Interacting Dark Energy
  Cosmologies
  Up-to-date cosmological data analyses have shown that \textit{(a)} a closed
universe is preferred by the Planck data at more than $99\%$ CL, and
\textit{(b)} interacting scenarios offer a very compelling solution to the
Hubble constant tension. In light of these two recent appealing scenarios, 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 state
in both the quintessential and phantom regimes. When considering Cosmic
Microwave Background data only, 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 solution
to current cosmological tensions, either by spoiling its effectiveness
concerning the $H_0$ problem, as in the case of Supernovae Ia data, or by
introducing a strong disagreement in the preferred value of the spatial
curvature, as in the case of Baryon Acoustic Oscillations.
