  Regularity properties of the pressure are related to phase transitions. In
this article we study thermodynamic formalism for systems defined in
non-compact phase spaces, our main focus being countable Markov shifts. We
produce metric compactifications of the space which allow us to prove that the
pressure is differentiable on a residual set and outside an Aronszajn null set
in the space of uniformly continuous functions. We establish a criterion, the
so called sectorially arranged property, which implies that the pressure in the
original system and in the compactification coincide. Examples showing that the
compactifications can have rich boundaries, for example a Cantor set, are
provided.
