A vein filter can switch from a collapsed state to a deployed filtering state and further from this filtering state to an open non-filtering state. The filter includes a plurality of primary filter legs and a plurality of secondary filter legs. The primary filter legs are grouped at one end in a common filter head. One secondary filter leg is connected to each of the primary filter legs in proximity of the filter head. Each secondary filter leg is connected to the adjacent primary leg to which it is not already fixed in proximity of the filter head by a connecting wire attached in the area of the free ends of the legs.
