Arb used as a verb in this way came about because.... Many years ago in the trading pits the brokers were given their orders to execute for customers by a "runner" whose job was to physically run orders from the desk to the broker in the pit. However, then came the game of index arbitrage where traders, off the floor would execute the basket of stocks that make up a index and then simultaneously take the other side of the trade in the index itself, resulting in a riskless profit. Because the transaction had to take place simultaneously, it was important that the Arbitrageurs got their order to the pit broker faster than "running it" so they invented a sign language that allowed their clerks on the phone to hand signal the order into the pit for a speedier execution. In the beginning, the only clerks using this sign language worked for the index arbitrageurs. And so, the verb arbing came about.
Arbitrage is relative. It's supposed to mean profiting in a no risk situation. But that is totally relative since everything has risk. Aside from that, not all price discrepancies can be arbed. The discrepancy must be greater than the costs of "arbing". These costs can be commissions, slippage, spread, and more. Hence, most arbs have a band around the price discrepancy, when it goes thru the band, or becomes too great, they take advantage of the arbitrage opportunity, because it means after costs, they will have a profit. They will have a profit if the discrepancy is corrected. This is why the markets are so called "effecient".