The article explores anisotropic connections in Finsler spacetimes, focusing on their relationship with pseudo-Finsler metrics. Vertically trivial Finsler connections are shown to be equivalent to anisotropic connections, offering a simpler interpretation. A new covariant derivative and parallel transport method are introduced, using a self-propagated vector as a reference for others. The Levi-Civita--Chern anisotropic connection is identified as the one preserving the length of parallely propagated vectors in pseudo-Finsler metrics.