Warning! this transaction is a double spend. You should be extremely careful when trusting any transactions to/from this sender.

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2 Answers
All valid transactions are relayed through the network. A client does not know which transactions will be a part of a block, so it stores and relays both double-spent transactions. If you regularly poll your bitcoind, you can see every transaction before it is put in a block. Then it is just a matter of checking txin data for duplicate inputs.

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The bitcoin network does NOT relay unconfirmed transactions that double spend other unconfirmed transactions, so neither blockchain.info not anyone else sees most unconfirmed double-spends. Nodes do not store two conflicting spends - they store only the first one they see.
This is becoming a bigger challenge for merchants because they need to connect to thousands of nodes in the hope of spotting double-spends.
The Bitcoin XT patch set is an early release of functions that are proposed for Bitcoin Core. It does relay double spends, and notifies the wallet of double-spend attempts that affect it.

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