I found all the transactions can be found publicly on blockchain, is that safe?
It shows from Address1 to Address2, and how many bitcoins, so everyone can find all the route, correct?
is it anonymous?
That's how Bitcoin works and that's the main strength of Bitcoin.
The whole transaction history is public - we call it block chain. Anyone in the world can have a complete copy of the block chain on computer. When new transactions happen, they're matched with all old transactions to make sure no Bitcoins are being spent more than once.
If you're worried about privacy,
there's not much to worry about. As far as you cover your tracks, it is not possible to link a Bitcoin address to a person. So even if the block chain shows a transaction from Address1 --> Address2, it is not known who sent the money to whom.
There's plenty to worry about. If you receive bitcoins you must share your address with whoever is sending you the bitcoins. At least they will know it's yours. If you're sending bitcoins then whoever you sent it to can see your address and know it's yours as well. If you trust either of these parties then no worries. but if you don't... Too bad.
Mixers can help obfuscate it if used right. That of course requires you to trust the mixer. If I were part of a three letter agency tasked with tracing bitcoin transactions I would set up the bestest
tm coin mixer in the world. I would guarantee you that no unauthorized entity will ever know what you did with your bitcoins.