In this paper we develop a novel technique to analyze both isolated and interconnected caches operating under different caching strategies and realistic traffic conditions. The main strength of our approach is the ability to consider dynamic contents which are constantly added into the system catalogue, and whose popularity evolves over time according to desired profiles. We do so while preserving the simplicity and computational efficiency of models developed under stationary popularity conditions, which are needed to analyze several caching strategies. Our main achievement is to show that the impact of content popularity dynamics on cache performance can be effectively captured into an analytical model based on a fixed content catalogue (i.e., a catalogue whose size and objects' popularity do not change over time).