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A recent surge of users migrating from Twitter to alternative platforms, such as Mastodon, raised questions regarding what migration patterns are, how different platforms impact user behaviors, and how migrated users settle in the migration process. In this study, we elaborate on how we investigate these questions by collecting data over 10,000 users who migrated from Twitter to Mastodon within the first ten weeks following the ownership change of Twitter. Our research is structured in three primary steps. First, we develop algorithms to extract and analyze migration patterns. Second, by leveraging behavioral analysis, we examine the distinct architectures of Twitter and Mastodon to learn how user behaviors correspond with the characteristics of each platform. Last, we determine how particular behavioral factors influence users to stay on Mastodon. We share our findings of user migration, insights, and lessons learned from the user behavior study.