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My experience was similar. I got nearly instant verification for tier 1, but that didn't let me make a deposit. I submitted all my documents that day, and have emailed support several times, however I am still waiting for verification over a month later.

How can I be anonymous with all these documents ?

Follow me @Yehey

After buying cryptocurrency, convert it to one of the ones that champion privacy on an exchange, send it to a wallet that you're not publicly connected to, and then no one knows who you are.