Deciding on web service equivalence in process-aware service compositions is a crucial challenge throughout the composition life cycle. Restricting such decisions to (activity) label equivalence constitutes a simplification for many practical applications: if two web services have equivalent labels, does this necessarily mean they are equivalent as well? In many scenarios other factors 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, we introduce the composition life cycle and discuss specific requirements for web service equivalence along its different phases. We define adequate equivalence notions for design, execution, analysis, and evolution of service compositions. Main focus is put on attribute and position equivalence. Altogether this paper is a first step towards a new understanding and treatment of equivalence notions in service compositions.