This paper deals with those time travels mostly considered by physics, namely those in the form of the so-called closed timelike curves. Some authoritative scholars have raised doubts about the status of these journeys as proper time travels. By using David Lewis’ famous definition of time travels proposed in 1976, we show that this proper status may actually be recovered, at least in some cosmological contexts containing spacetime regions, such as those concerning black holes described by the Kerr–Newman metric, that (...) allow the formation of local closed curves. But, the mathematical incompatibility between ordinary black hole solutions to Einstein field equations and the cosmological solutions induces us to take into consideration the more general issue pertaining to the slippery interplay between models related to local and global aspects of the world, highlighting, in particular, the different notions of time that these domains inevitably imply. This leads us to think that time is not a univocal entity of the world, but is a scale-related characteristic which claims the adoption, when investigating its ontological status, of a sort of regional approach. We also briefly dwell upon the most appropriate form of realism that such a kind of dispute between local and global models may involve. (shrink)