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.
Also, this means that fundamental assumptions and the calculations are hidden from view. Recently, some physicists questioned the findings of LIGO but if I understand correctly all is decided by data analysis software and outside teams have a disadvantage to decipher it.