Yep. Start by removing the cable from the carb and move the linkage on the carbs through it's full range. See how smoothly it operates. If it is ok, have someone gently step down on the gas pedal while you hold the end of the cable or linkage, putting some resistance on it. See if you can detect any binding in the movement.

If you did encounter sticking when you just did the carbs by themselves, you need to find out which carb is the offender. Remove the linkages between them, and operate them one at a time to see which one is binding.

Like any diagnostic job, you are doing process of elimination. Keep removing items from the mix until the bad one shows up.

Don