Sorry if the title is confusing, here is what I mean.
I recently threw some fiats in Kraken and invested in Bitcoin, the first interrogation I had was "Can I see my transaction publicly on the internet if I could find the right block used for it?".
But on a large scale this interrogation translates to "Is each exchange platform implementing their own clone of the Bitcoin specs or is there a general blockchain that rules the entire decentralised financial system?"
As long as your Bitcoins are in Kraken and you haven't withdrawn them, then the Bitcoins aren't actually recorded on the blockchain -- Kraken just has a line in their database saying they owe you a certain number of Bitcoins. You wouldn't find this on the blockchain until you actually initiate a withdrawal of your Bitcoins from Kraken.
Every Bitcoin exchange, and every Bitcoin user in the world, when they do publish to the Bitcoin blockchain, publish to the same blockchain though.
