When miners M1 and M2 compete to mine block B and miner M2 mines it just after miner M1, his mined block is called ommer/uncle/orphaned. I read that these blocks (untill sixth generation) can be included in the blockchain. Does this mean that transactions of block B are included twice?


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No. Only uncle block headers are included. Also when including uncles only the validity of their headers is checked, transactions are ignored. From Design Rationale:

Uncle validity requirements: uncles have to be valid headers, not valid blocks. This is done for simplicity, and to maintain the model of a blockchain as being a linear data structure (and not a block-DAG, as in Sompolinsky and Zohar's newer models). Requiring uncles to be valid blocks is also a valid approach.

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