The LIGO result is actually excitingly available as an IPython notebook, which provides a tutorial to verify the data yourself, using entirely open source software. https://www.gw-openscience.org/s/events/GW150914/GW150914_tu... The actual signal processing isn't that complex IMO.

I don't know how open the LIGO hardware is, but it's very unlikely you would build one yourself to verify.