Can anemia spread from person to person?

No: No, anemia is lack of sufficient blood/hemoglobin in the system. It does not spread from person to person but some forms of anemia (ex. Thalassemia) can be genetic, i.e. Transmitted from parents to children.

No: Anemia itself is not contagious so it does not spread from person to person; however, other conditions that cause anemia like infections can do that. In other words, if a person has an infection they may also become anemic. If the infection is transmitted to somebody else and that person also develops anemia, it may look like the second person "got" anemia from the first.