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I'm trying to understand how bitcoin transactions work. From what I understand, in the Bitcoin network nodes hold different versions of the Blockchain and after some time the different chains start converging to form the main chain (longest sequence is preferred).

Here's a scenario. Node A is holding a chain which is not in sync with the rest of the nodes and node A decides to post a transaction. The miners will pick up this transaction and add them to a block in their own chain which is different than Node A's chain.

So now when Node A looks at the network, will it just ignore its own inconsistent chain and pick the miners' chain? Will the transaction made by node A even show up in the blockchain?

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Node A is holding a chain which is not in sync with the rest of the nodes and node A decides to post a transaction.

Your node, that is not synced, will only let you spend outputs that it has validated as unspent. So in your scenario step 1 may not be able to happen depending on age of the UTXO and what block your node is at. An old node that is not synced can only spend old coins that haven't moved.

A more detailed answer from A. Chow: https://bitcoin.stackexchange.com/a/91822/26873

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Node A is holding a chain which is not in sync with the rest of the nodes and node A decides to post a transaction.

If node A created transaction from valid unspent UTXO (which is valid on longest chain), the transaction will be valid. You don't have to be even a node to send this valid, signed transaction, you can mail it to the node C which will include it into mempool.

The miners will pick up this transaction and add them to a block in their own chain which is different than Node A's chain.

As long as your node has communication with these miners, yes (there are different scenarios of "unsyncing", I assume hardforks as well, but I guessed you meant orphan blocks mostly, or lack of recent blocks?).

So now when Node A looks at the network, will it just ignore its own inconsistent chain and pick the miners chain?

No. If you are looking at top of chain A which isn't in sync with the longest chain, where miners should add the transaction, your node won't see it. The rest of the network on the longest chain will observe it though.

Will the transaction made by node A even show up in the blockchain?

Yes, in the longest chain.

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