Various aspects of the disclosure pertain to blood vessel occlusion devices having a central longitudinal axis and comprising: (a) a hub, (b) a self-expanding support frame comprising a plurality of wire segments forming a plurality of cells, and (c) a covering material covering cells within the transition portion. The support frame may be self-expandable from a constrained shape to an unconstrained shape that comprises (ii) a substantially cylindrical portion having a diameter and an axis that is coincident with the central longitudinal axis, the substantially cylindrical portion comprising a first ring of the cells extending in a 360° rotation around the central longitudinal axis and (ii) a transition portion disposed between the substantially cylindrical portion and the hub. Other aspects for the disclosure pertain to assemblies, kits and methods that employ such devices.
