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?"