Different Timelines

Each particular future history series presents a single linear timeline that differentiates that series from any other. Thus:

in Poul Anderson's Psychotechnic History, a near future nuclear war leads to a UN world government;

in Anderson's Maurai History, a near future nuclear war leads to the Maurai Federation;

in Anderson's Technic History, a period called the Chaos is followed by the transition from Western to Technic civilization.

These fictional futures are equally valid but mutually incompatible although partially parallel. We can imagine that the different histories unfold in parallel timelines. We might even compile comparative chronologies in parallel columns. However, most relevant texts do not encourage any parallelism. Some later volumes by Heinlein do refer to a multiverse but I do not accept anything after Orphans Of The Sky as a valid contribution to the Future History even though written by Heinlein himself. 

In Anderson's "House Rule," Nicholas van Rijn from the Technic History visits the inter-universal inn, the Old Phoenix, and Anderson's "Losers' Night" informs us that Rhysling from Heinlein's Future History has also been there. However, these two stories are outside the future histories which is appropriate since the Old Phoenix is outside the timelines. The two Old Phoenix stories have closer links to two fantasy alternative histories than to the future histories. This is the point at which Anderson's works come closest to forming One Big Series although they never do that because most of his series and individual works remain self-contained narratives and there are a lot of them.