The blockchain is public, yet a Bitcoin wallet can be created anonymously. So are Bitcoin transactions anonymous? Not at all…
Each transaction into and out of a wallet is a bread crumb. Following the trail is trivial. Every day, an army of armchair sleuths help the FBI. That’s how Silk Road was brought down.
The problem is that some of that money eventually interacts with the real world (a dentist is paid, a package shipped or a candy is purchased at a gas station). Even if the real-world transaction is 4 hops before or after hitting the “anonymous” wallet, it creates a forensic focal point. Next comes a tax man, an ex-spouse or a goon.
The first article linked below addresses the state of tumblers (aka “mixers”). They anonymize an open network by obfuscating the trail of bread crumbs.
Mixers/tumblers aren’t the only way to add a layer of privacy to Bitcoin transactions. The Lightning Network spec includes an optional 17-hop onion routing (just like TOR’s 4 step onion routing). I have not yet seen the feature expressed in wallets or services, but if implemented, it will be even more private and trustworthy than a mixer, because there is no middle party to trust (by you) or squeeze (by investigators). It has the potential to makes any crypto Bitcoin even more anonymous than cash.
Certain cryptocurrencies (not Bitcoin) have anonymity baked in by design. Monero, ZCash and Dash are privacy tokens that use very different approaches to eliminate the bread crumbs. Monero appears to have one distinct advantage: Like the TOR network, it is trustless. But there are benefits to each approach.