When I start withdrawing and depositing big amount of money into the bank accounts, will I be in trouble with the tax offices?
You won't get in trouble with the tax offices as long as you properly report your income and pay your taxes. So for tax purposes you will need to keep track of your arbitrage trades and the profits you made. You will also need to be able to proof these trades. In case beneficial holding periods apply, you will have to decide whether you calculate your profits using the FIFO (first in first out) or LIFO (last in first out) principle -- and stick to it.
Your bank may cause you some problems in that you may trigger their fraud department and could be asked in detail to explain on where the transactions are coming from. Anecdotally banks have supposedly shut down or frozen customer's accounts due to cryptocurrency related bank transactions. Keep in mind that your bank is likely to forward any information on larger money movements to your local tax authorities either way, especially if these transactions show a change in your usual account usage.
Depending on the amount of money and where you live you might need to notify your bank and authorities in advance of such transactions (for example in Germany any border-crossing transaction of EUR 12,500,- or beyond needs to be reported).
Does anyone know if have to pay taxes in both countries?
You will have to pay taxes in whatever country you are tax resident, regardless of where you bought or sold the coins. If you ever had ties to the US, but are now tax resident of another country, you might get twice the paper work but will likely only have to pay taxes in the country where you reside.
Disclaimer: Not an expert, everything I mentioned is only a general rule of thumb from my own layman experience and will highly depend on your individiual situation. If you are serious about running arbitrage at scale (monthly trading volume at 3-4 EUR/USD digits or beyond) I'd recommend getting a tax advisor.
