Just to be clear, which arrows are you talking about? If it's the up and down arrows, those are the actual data transfer indicators. But you said circular arrows, which are the sync arrows. If it's flashing, it means something on the phone is sync'ing with its servers. I.E. your Google Contacts list, some messenger apps, ect. I think it is supposed to only do it periodically. If it's flashing all the time, then something may be stuck in a sync mode. There is a way to globally turn sync on and off for all apps. I don't remember the basic way to do it via the settings menu, but I use the built in Power Control widget and it has a sync button on it. Otherwise, you need to go through each app and turn its sync option on/off (if applicable) one at a time.
Personally, I don't have anything that needs sync'ed very often, so I just keep it turned off globally and only turn it on if I've updated something like my contacts list. Once it's done, I turn it back off to save on my batter and data.