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In my experience, a lean condition due to an intake manifold leak would more likely cause popping through the carb rather than back firing through the exhaust. Back firing comes from gas fumes building up in the exhaust, either from a rich condition or from intermittent firing caused by an electrical/ignition problem.
Checking for a rich condition is a super easy test to perform. Get it warmed up to where it's idling rough, and then shut off the petcock. If it starts to smooth out and idle better as the fuel level drops in the float bowl, then it's a rich condition issue (possibly just a bad needle/seat).
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