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Wouldn't it better to send bitcoins through out the chain of say five-six exchanges (where you have anonymous accounts) , return them back into wallet and then we're there? Each exchange would act as a kind of mixer in this case.
Could you name 5-6 anonymous exchanges? The only one i can think of is binance (which does chain analysis, so you'll need to find some more exchanges to effectively mix your coins), and yobit, which i find particularily untrustworthy.
Another problem is that most of these exchanges usually ask for .5 or 1% withdrawal fee. multiple that by 5x, or 6x, and you'll be paying massive amounts of fee for what might be just very little improvements in privacy.
Will exchange #1 send to exch #2 the same bitcoins that were received from me? I don't think so, IMO, they will differ from mine, every next exchange belonging to my chain will continue in that, or am I wrong on that?
Agree, that could impose extra costs compared with the mixers.
Well, they probably won't exchange/send the same bitcoin back to you, but that doesn't mean that they don't know the origin of the funds. Especially exchanges such Bitstamp, coinbase, and kraken all use third party chain analysis products, and probably share/won't hesitate to share that info with authorities/other exchanges.
Which means that, yes, the chain might look broken, but these exchanges can and will still keep track of the coins, especially if it's significant amounts not used for trading and send through regulated exchanges as mentioned above, and share that info to LE/other exchanges, which in turn will probably result to the funds being linked.
Hence why i don't think this is such a smart idea, apart from it costing a lot of $$$, and exchanges who probably won't be too happy about it.