What is annual recurring revenue?
Annual recurring revenue is a type of revenue that is generated from subscriptions for either goods or services. The software product that you pay for monthly would have an ARR, and so would your service contract with your HVAC company. Annual recurring revenue applies to anything that you would pay periodically to use, provided that the period is regular and the use or service is consistent, based on your agreement with the company.
So, the regular servicing that you have for your HVAC system, which might include twice-yearly basic maintenance of your system, could be considered part of the HVAC company's ARR, but the full service that results from the maintenance turning up a serious problem would not.