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If I want to make a transaction with someone via Tumblebit, would it be visible on the blockchain?
If a have a known public bitcoin address and I will move bitcoins from there to pay someone via Tubmlebit, will it be recognizable?
If I receive payment that went through tumblebit, would that be recognizable from the history of transactions?
How exactly would that look?
All confirmed transactions are publicly visible on the blockchain.
What's probably far more interesting for you is whether anyone can find out whether you put your money through Tumblebit.
What you really need to know is in this sentence of the paper you linked to:
Specifically, while the blockchain reveals which payers and payees participated in an epoch, no one (not even the Tumbler τ) can tell which payer paid which payee during that specific epoch.
Tumblers are recognizable on the blockchain. If you pay someone via Tumblebit from an address which is publicly known to be yours, people will know that you paid someone via Tumblebit. They won't know who you paid but just know that you paid someone via Tumblebit might be enough to raise suspicion.
If you receive payment through Tumblebit, people can find out you received it through a tumbler. But they won't know who the "you" in the previous sentence is until you somehow reveal your identity. Until then, it's just that money went to someone. Who that someone is, isn't known to the public. But if your next transactions goes to an online shop with a order to ship a parcel to your home, you can be pretty sure the merchant knows that the address he received the payment from belongs to you.
The fact that people know that money went through tumblers simply emerges from the fact that tumblers want to get money from a lot of people involved. Look at transaction f653dc8cf567b6cf0cf98660a66a1b138677388c16c87b8f4d68f5979cd4627f. I just looked for one to show to you in the newest block and came across it. It moves money from 13 addresses to 13 different addresses. And not exactly little: The equivalent of 2.5 k$. Moving money from 13 addresses to 13 different addresses isn't exactly how a transaction of someone who just bought a computer for 2.5 k$ on tigerdirect.com would look like, is it?
If you look at how the input addresses got their funds, it gets even more suspicious. For example, 1HjfSKDVnKDsJBWWDWcgcmGDDhauc7cR8q got its funds from 19 addresses. It doesn't seem like this just happened by random chance, does it?
You might also want to take a look at this question and at this one.
