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Deciding on Web service equivalence in process-aware service compositions is a crucial challenge throughout the composition life cycle. However, restricting such decisions to activity label equivalence is not sufficient for many practical applications: if two activities and Web services respectively have equivalent labels, does this necessarily mean they are equivalent as well? In many scenarios e.g., evolution of a composition schema or mining of completed composition instances, other factors also play an important role. Examples include context information e.g., input and output messages and information on the position of Web services within compositions. In this paper, the authors introduce the whole composition life cycle and discuss specific requirements for Web service equivalence along its different phases. The authors define adequate equivalence notions for the design, execution, analysis, and evolution of service compositions. This paper focuses on attribute and position equivalence and contributes a new understanding and treatment of equivalence notions in service compositions.