The carby models had a mass of tubes going all over the place, early PGM-FI's weren't much better. That particular vacuum valve is as Sp33 says, draws warmed air off the exhaust headers to help vaporise the fuel entering the engine on and just after start-up. The warm air hose is that one underneath with the insulation wrapped around it. Provided it's working correctly, that valve will open fully once the engine reaches temperature to let air through from the filter. There will be a water heating connection, sometimes directly from the head (or by hoses) to the inlet manifold that takes over the heating. Emissions control stuff that's removed can cause all sorts of problems for daily driving. If it was a dedicated race car being run WOT, might be different.