[Sid Squid]

Sounds very much like either fuel starvation or contamination. Drain the carb float bowls, it's not easy to get a container under the carb to collect the fuel such that it might be examined, but if one drops loads and the other very little, it may give an indication of what the fault is. Early SVs are prone to water in the fuel from corroded tank drains, as the years pass the problem gets worse.
There is a fuel pump, it's on the frame rail to the right of the carbs, it rarely gives trouble though so I wouldn't start there. Testing is easy though, it's vacuum operated so does the outlet give regular doses of fuel as you turn the engine over? If yes, it's very probably fine. If no, then blow through the inlet and outlet whilst blocking the other, listen very carefully through a hose connected to the vacuum connection - any hissing and the diaphragm is holed. Rebuild parts are available aftermarket if needed, Suzuki don't supply them.