I will show and discuss how the location of the Local Group with respect to
the local Cosmic Web influence the properties of galaxy velocity correlation
statistics. We will demonstrate how and up to what scales various properties
of the LG-like environment correlate with the nearby galaxy velocity field.
The effects we show have profound implication for cosmological
analysis of the local galaxy velocity data. The galaxy peculiar velocity
field has been shown to offer a potentially strong ans stringent cosmological
test of GR. The LG observer bias will have to be included into a careful
analysis of the existing and incoming galaxy velocity data in order to allow for precision cosmological and gravity tests.