How did the Reapers invade the galaxy in Mass Effect 3?

We all know that the Reapers are going to invade the Milky Way in ME3, but one question still remains! How did the reapers get there so fast? Sovereign is dead, and can therefore no longer activate the citadel mass relay. The keepers ignore the reapers, and the collectors were wiped out by Shepard, plus loosing the Alpha Relay in the Bahak system, thus exterminating all chances of a quick invasion of the galaxy. But apparently they found a way, and a really fast one at that, because they invaded Earth pretty much right after the events in ME2. Any thoughts on this? was just wondering about it today, and wanted to hear you guys thoughts on it.