Boolean networks are a class of qualitative models used extensively to model regulatory interactions driving biological processes. While structurally simple, their dynamics can be quite complex. One recurrent issue in studying the dynamics of these models is state explosion. To tackle this problem model reduction techniques are employed. These techniques aim at producing smaller models that behave approximately as the original model. In this paper, we use Abstract Interpretation, a unifying framework to compare semantics of models at different levels of abstraction. Here, we relate the behaviors of the initial and reduced models for two model reduction approaches, a new method and the classical one proposed by Naldi et al.. In both cases, we formally characterize which traces are preserved by construction.