Complex sentence: After his release in the 2001 summer, Vargas moved to F.C. Alverca, experience his most steady period in his country, with three consecutive topflight seasons, being relegated in 2003--04.
Split into simpler sentences: After his release in the summer of 2001, Vargas moved to F.C. Alverca. There, he would experience his most steady period in his country, with three consecutive topflight seasons, being relegated in before 2003--04.