Thermodynamic formalism for suspension flows over countable Markov shifts

We introduce a new notion of topological pressure for suspension flows over countable Markov shifts. We show that our definition, which is a natural analogue of Gurevich pressure for a Markov shift, is equivalent to previous notions of topological pressure which were defined on a restricted class of flows. We also widen the domain of definition of these previous notions, making them suitable for application to some important examples.