Home AC Clicking Sound Help

Occasionally the air handler will make clicking sounds when turning on. During this period the air flow is noticeably decreased. After varying lengths of time, the clicking stops & the air flow increases to normal rates. From what I've read, it could be a relay or thermostat issue. I changed the thermostat battery, but I don't expect it to resolve the issue. I'd appreciate guidance on how to troubleshoot the issue. The unit is covered by a home warranty, but I would like to narrow down the issue before some random company attempts the repair.