How do large interferometers work? In very large Michelson interferometer a such as LIGO, how can we keep the two light paths at the exact same distance in order to avoid any unwanted and noisy fringes shift? 
When I used to make Michelson interferometers, I encountered a lot of problems with temperature variations, residual vibrations or air convection. 
I can't imagine how possible it is to get a stable signal from a 4km long interferometer. 
What is the secret? 
 A: Interferometers don't measure absolute distances.  Interferometers measure changes in distance at the scale of the wavelength of light.
The gravitational wave event observed by LIGO in September had a strain of $10^{-21}$.  This doesn't mean that the length of each arm is known to twenty-one significant figures, as you seem to be assuming; it means that when one mirror moves away from the beam splitter and the other mirror moves towards it, the difference can be measured with high precision.  Think of it like the beam balance: it's possible to tell which item in a balance is heavier, and by how much, by the angle at which the balance reaches equilibrium, even if neither absolute weight is known.
LIGO's interferometer is exceptional because the the light in the interferometer has wavelength $\rm 800\,nm \approx 4\,km \cdot 2\times10^{-10}$, so that the observed strain corresponded to roughly $10^{-11}$ wavelengths.  This is still a parts-per-trillion measurement!  The main feature that makes this possible is that each arm of the interferometer is a Fabry-Perot cavity, which multiplies the effective length of the interferometer by a factor of about 300.  I believe (but haven't found a citation) that the sensitivity to strain goes like a factor of $(300)^2 = 10^5$, since you get one factor from the extra length and another factor from the gain of the Fabry-Perot cavity.  That means LIGO is measuring relative changes in the length of its unfolded arms to only a millionth of a wavelength, which sounds hard but not nearly as bananas as an absolute length measurement to twenty-one decimal places.
