The meaning of Blood Line from the Oxford Dictionary.
Blood - Parentage.
Line - Several generations of a family.
Generation - A single stage in decent or pedigree, three generations.
Stage - A point or period in the course or development of some thing.
If look into the dictionary further ( Parentage,Ancestry,Ancestor) you will find that all of Joe Blogs birds need to be related before you can say they are Joe Blogs Blood Line.