  We study the thermodynamic formalism for suspension flows over countable
Markov shifts with roof functions not necessarily bounded away from zero. We
establish conditions to ensure the existence and uniqueness of equilibrium
measures for regular potentials. We define the notions of recurrence and
transience of a potential in this setting. We define the "renewal flow", which
is a symbolic model for a class of flows with diverse recurrence features. We
study the corresponding thermodynamic formalism, establishing conditions for
the existence of equilibrium measures and phase transitions. Applications are
given to suspension flows defined over interval maps having parabolic fixed
points.
