Engine Exhaust System problems of the 2000 Mazda Millenia

I own a 2000 Mazda Millenia s model. My Millenia has the lysholm supercharger (s/c). Recently, the car has begun to blow blue smoke out the exhaust pipe at startup. The smoke at startup last for about 15-30 seconds. I took the car into the local Mazda dealer. The Mazda mechanic removed the front intercooler and front intercooler pipe. The mechanic said there was oil in the intercooler and the intercooler pipe. He said this indicates the lysholm s/c is leaking. He said the lysholm s/c has a bad seal. Yet, he said he has never taken a lysholm s/c apart and does not know which seal is leaking. He said Mazda just replaces the entire lysholm s/c. A new lysholm s/c is approx. $7000 cad. My car has the 5 yr /100,000km (62,500 miles)power train warranty. The power train warranty states it covers ". . All internal parts". . . And ". . All gaskets and seals. . ". The seal failed inside the s/c, therefore I believe the s/c seal and its replacement should be covered under the power train warranty. Mazda disagrees with me, though Mazda is willing to pay 50% of the cost of a new s/c. Mazda has issued an m-tip (similar to a TSB) for problems with oil leaking from the s/c. The remedy is to replace the s/c. I feel Mazda knows the s/c is prone to leaking prematurely.

When starting the vehicle at a cold start, after the engine was cooled, white smoke emitted from the tail pipe.