Neighborhood effects have been demonstrated to play a significant role in determining resident' access to health, education, and economic mobility. The study of the neighborhood change is pertinent to the understanding of the processes as well as the consequences of gentrification and displacement, and urban revitalization. Recently, Optimal Matching (OM) is increasingly used for analyzing urban neighborhood change. Originally developed for matching DNA sequences in biology and analyzing strings in computer science, OM works by finding the minimum cost of transforming one sequence to completely match the other using operations like substitution, insertion, and deletion. The minimum cost is considered as the distance or dissimilarity between these two sequences. The first application of OM in social sciences was found in the life course research. Having recognized the inherent difference in DNA and life course sequences (that is, while the former have common ancestors, the latter are governed by an unfolding process), social scientists have proposed various variants of OM to better suit the life course study and to reveal different characteristics of life courses, like timing, sequencing, and duration. The current application of OM to evaluate the distance/dissimilarity between neighborhood sequences has benefited a lot from its application to the life courses. However, we argue that a neighborhood sequence is fundamentally different from a life course sequence (like a family life trajectory or a professional career trajectory). While the latter is formed by natural categorical life events, the former is a construct in that the neighborhood types are usually the outcome of clustering multiple census tract-level socioeconomic characteristics. In this article, we propose a variant of OM which considers neighborhood dynamics as an unfolding process and explicitly treats neighborhood sequences as a construct by utilizing the vital information of neighborhood differences in setting the costs of OM operations. In addition, in the OM process, we extend the definition of neighborhood stability based on the empirical transition rates between neighborhood types. We demonstrate the advantage of the proposed OM variant in uncovering the sequencing and stability structure in the neighborhood sequences via a case study of the Los Angeles metropolitan area from 1970 to 2010.