In recent years, Software Transactional Memory systems (STMs) have garnered significant interest as an elegant alternative for addressing concurrency issues in memory. STM systems take optimistic approach. Multiple transactions are allowed to execute concurrently. On completion, each transaction is validated and if any inconsistency is observed it is aborted. Otherwise it is allowed to commit. In databases a class of histories called as conflict-serializability (CSR) based on the notion of conflicts have been identified, whose membership can be efficiently verified. As a result, CSR is the commonly used correctness criterion in databases. Similarly, using the notion of conflicts, a correctness criterion, conflict-opacity (co-opacity) which is a sub-class of can be designed whose membership can be verified in polynomial time. Using the verification mechanism, an efficient STM implementation can be designed that is permissive w.r.t co-opacity. By storing multiple versions for each transaction object, multi-version STMs provide more concurrency than single-version STMs. But the main drawback of co-opacity is that it does not admit histories that are uses multiple versions. This has motivated us to develop a new conflict notions for multi-version STMs. In this paper, we present a new conflict notion multi-version conflict. Using this conflict notion, we identify a new subclass of opacity (a popular correctness-criterion), mvc-opacity that admits multi-versioned histories and whose membership can be verified in polynomial time. We show that co-opacity is a proper subset of this class. The proposed conflict notion mv-conflict can be applied on non-sequential histories as well unlike traditional conflicts. Further, we believe that this conflict notion can be easily extended to other correctness-criterion as well.