was driving the other day, turned the heater on and the heater turned off and then turned back on, same for ac as well.
is this a fuse issue, heater core or fan issue.

 

could be fan motor or fan motor relay about to go out, pretty easy fix. If it was fuse it would just stay off.

 

I agree, this sounds like the most logical explanation right off hand. The Blower motor is probably going in and out causing the fan to turn on, then off. Which will give you the symptoms of the A/C cutting on and off as well as the heater. When the fan turns off you have no air flow over either the A/C Evaporator or the Heater Core which means no A/C and or Heat.

I have never had to dig into those relays or troubleshoot them but I have "heard" it can be quite common for the relay(s) to malfunction leaving some of your blower fan settings useless(IE: 1 and 2 fan settings might not work at all but 3 and 4 will work normally.) You might have a relay problem that is messing with all the settings intermittently.

 

I'm having the same problem. But mines is the black 12volt fuse in the fuse box(engine bay) I've changed 2 so far. They keep blowing. 3 weeks ago the 1st one went then the 2nd one lasted another 3 weeks. Any ideas what could be causing it?

 

took a look at the relay today kinda just blew it off but now that thing is getting annoying, so I'm trouble shooting the relays tomorrow morning.

 

92-95 Civic? There's only one blower motor relay. You should also consider the blower motor itself and the fan switch.