I’m guessing a permit is normally pulled there, for any new HVAC systems installed. Who am I fooling...a permit is probably needed in SF to swap out a light bulb. Anyway, under-the-table installations would have to occur for new gas heaters because SF wouldn’t issue a permit. That would turn into a real mess.
I had a new gas furnace installed, bought it and trolled those in the heating business for a hungry employee. I ended up saving $3,000 on the install, and money on the purchase price of the furnace. I helped haul the old one out and the new one in. It was an under the house install. It took less than 4 hours. His employer, had they did this would have made $5K for one days labor for a journeyman and an apprentice. Then add on the permit to turn off the gas and use the gas sniffer after it is on. HINT, you use a Crescent wrench and rotate the on/off switch like at the water meter.
I wouldn’t do a furnace but water heaters are very easy to install.