Stellar parallax is used to "verify" that the Earth is moving but it's dependent upon the A priori assumption that the Earth is moving. In case you weren't sure, that's circular reasoning.
Stellar Parallax
Relative Motion
There's no observable difference between heliocentric and Geocentrospheric models because they're two frames of reference in the same system. They coexist.
Measure the Heavens
We start with a simple observation: God hasn't, and won't, cast off the seed of Israel. This leads us to a conclusion: We haven't measured the heavens. So why do we think that we know the distance to the sun and its mass?