Future Cosmic Microwave Background experiments together with upcoming galaxy and 21-cm surveys will provide extremely accurate measurements of different cosmological observables located at different epochs of the cosmic history. The new data will be able to constrain the neutrino mass sum with the best precision ever. In order to exploit the complementarity of the different redshift probes, a deep understanding of the physical effects driving the impact of massive neutrinos on CMB and large scale structures is required. The goal of this work is to describe these effects, assuming a summed neutrino mass close to its minimum allowed value. We find that parameter degeneracies can be removed by appropriate combinations, leading to robust and model independent constraints. A joint forecast of the sensitivity of Euclid and DESI surveys together with a CORE-like CMB experiment leads to a $1\sigma$ uncertainty of $14$~meV on the summed neutrino mass. However this particular combination gives rise to a peculiar degeneracy between $M_\nu$ and the optical depth at reionization. Independent constraints from 21-cm surveys can break this degeneracy and decrease the $1\sigma$ uncertainty down to $12$~meV.