You can display a single centerline section (or a range of sections) in 3D Slicer. Just drag-and-drop the vtp file to the application window, cick OK, then go to Models module / Scalars section, enable "Visible" and "Threshold", and adjust threshold range.
Alternatively, if you compute centerline using SlicerVMTK extension's "Extract centerline" module then you can choose to create "Network curve" or "Centerline curve", which builds a curve hierarchy, where you can select/delete/show/hide each individual centerline segment.
Andras