Complex sentence: Six days before the race began, RCS Sport (the organizers of the Giro) reversed themselves and invited Astana, a decision which was at least partly contingent on Contador, Leipheimer, and Klöden participating in the race.
Split into simpler sentences: Six days before the race began, RCS Sport (the organizers of the Giro) went back on the decision to exclude Astana and extended them a late invitation. This change of heart was at least partly contingent on Contador, Leipheimer, and Klöden participating in the race.