Does the tax service actually make a sum of all the deposits you had during the year?
Yes, but they also sum all the
withdrawals you had during the year. If they notice that you're sending about the same amount of money
to several exchanges as you receive
from them, they're going to pay more attention to the
difference than the total. And since that difference should about the same as the profit you've declared, they're not likely to trouble you.
How do i prove that? All the exchanges keep logs but i doubt i could just send these to the tax service...
Why would you doubt that? If you do happen to get audited, the exchange logs are exactly what the tax service will ask for (and remember, they can request the same logs from the exchanges themselves, just to keep you honest).