Which of these database designs is normalized? I have two possible database designs. 

A) a many-to-many relationship between Branches and FiscalYears via a dedicated join table FiscalYearsBranches

B) two (or more) many-to-many relationships between Branches and FiscalYears via other tables (Documents, Factors, etc.)

See the diagrams below. Which of these designs is better and why?



Design A:  a many-to-many relationship between Branches and FiscalYears via a dedicated join table FiscalYearsBranches







Design B: two (or more) many-to-many relationships between Branches and FiscalYears via other tables (Documents, Factors, etc.)
Design A implies a relationship between FiscalYears and Branches which exists separately to the relationships between these tables and Documents and Factors. This relationship is recorded in FiscalYearsBranches

Design B does not do this, it only defines relationships between FiscalYears and Branches via Documents and Factors. 

You should think about the relationship between FiscalYears and Branches: if this exists, as a real life relationship you can talk about outside of the database, even when you're not looking at Documents or Factors, then go with A. If not, go with B, otherwise you are suggesting that this relationship exists when it doesn't.