“Connection Gas” is distinct increase of gas above a normal background gas level when bottom up occurs after a connection. If you see a small high gas peak in short period of time and when you calculate back you will see that it comes from every connection, you can suspect that this is the Connection Gas.
The connection gas occurs because total pressure (hydrostatic pressure + friction pressure) temporarily decreases during making connection. Basically, it means that you lose equivalent circulating density due to pumps off. In addition, the connection could be happened because of swabbing effect when the drill string is worked off bottom prior to making connection.
The connection gas can indicate that pressure between hydrostatic pressure exerted by drilling fluid and formation pressure is almost in balance condition. Therefore, when you see the connection gas, you should consider weighting up mud in the system before resuming drilling operation or tripping operation.
Reference book: Well Control Books