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During the past decade, significant international and broader interdisciplinary research is increasingly carried out by global collaborations that often share resources within a single production e-science infrastructure. More recently, increasing complexity of e-science applications embrace multiple physical models (i.e. multi-physics) and consider longer and more detailed simulation runs as well as a larger range of scales (i.e. multi-scale). This increase in complexity is creating a steadily growing demand for cross-infrastructure operations that take the advantage of multiple e-science infrastructures with a more variety of resource types. Since interoperable e-science infrastructures are still not seamlessly provided today we proposed in earlier work the Infrastructure Interoperability Reference Model (IIRM) that represents a trimmed down version of the Open Grid Service Architecture (OGSA) in terms of functionality and complexity, while on the other hand being more specifically useful for production and thus easier to implement. This contribution focuses on several important reference model invariants that are often neglected when infrastructure integration activities are being performed thus hindering seamless interoperability in many aspects. In order to indicate the relevance of our invariant definitions, we provide insights into two accompanying cross-infrastructure use cases of the bio-informatics and fusion science domain.