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The Maximum Parsimony (MP) problem aims at reconstructing a phylogenetic tree from DNA sequences while minimizing the number of genetic transformations. To solve this NP-complete problem, heuristic methods have been developed, often based on local search. In this paper, we focus on the influence of the neighborhood relations. After analyzing the advantages and drawbacks of the well-known Nearest Neighbor Interchange (NNI), Subtree Pruning Regrafting (SPR), and Tree-Bisection-Reconnection (TBR) neighborhoods, we introduce the concept of Progressive Neighborhood (PN), which consists of constraining progressively the size of the neighborhood as the search advances. We empirically show that applied to the MP problem, this PN turns out to be more efficient and robust than the classic neighborhoods using a descent algorithm. Indeed, it allows us to find better solutions with a smaller number of iterations or trees evaluated.