No. Unfortunately it's not relative to anything. Nasim Haramein, the guy behind that animation/idea, is a known physics quack. In the future I would suggest being skeptical of anything coming from his "institute": The Resonance Academy (http://resonance.is/)
It looks like it's largely correct [scale excepted] relative to a fly-by following the solar system relative to a point moving away from the sun on a perpendicular to the plane of the solar system.
Isn't one of the points of relativity that we can choose any point as an origin - in the gif are the motions relative to the sun [scale excepted] largely correct?
The main problem the sibling comment notes is that the plane _if_ it were following the orbit of the sun around the galactic centre it would be inclined by 60 degrees to motion along the orbit [they also note problems with exaggeration of the motion of the sun in its vertical motion (relative to the galactic plane) and in the precession of the plane of the solar system]. That doesn't make the gif wrong in itself, it just makes it not what people might assume it is.
Fastidious pedantry, sorry.
If we're going to be right lets be as right as we can; so please post corrections if I'm wrong at all.
All that aside I'd be really interested in seeing a simulation of the galaxy that matched observations for the precession of the solar system, movement of the planets, movement of the sun around the galactic centre. Does such a thing - that can be run at home - exist?
Relativity does tell us that there are no preferred inertial reference frames. But the comment I replied to was asking about a very specific reference frame: the galactic center.
And to one up your pedantry: relativity allows us to define our coordinate system in any inertial reference frame to compare with other inertial reference frames. The solar system orbiting the galactic center is not inertial since it is constantly accelerating.
The GIF makes it look like the planets are trailing behind the Sun, which they are not at all. They orbit, so they constantly pass in front of it as well as behind it relative to its movement in the galaxy.
