# h-principle for pairs

Let $$A,B$$ be complex analytic spaces. Suppose that $$[A,B]$$ satisfies the h-principle: i.e. every class of continuous function $$f:A \to B$$ up to homotopy, contains a holomorphic representative. Let $$C \subset A$$ and $$D\subset B$$ be submanifolds (not necessarily complex).

Let $$[(A,C), (B,D)]$$ be the class of continuous functions $$f:A \to B$$ with $$f(C)=D$$ up to homotopy (where homotopies are required to preserve the relative parts).

When does exist a h-principle for $$[(A,C), (B,D)]$$? Or more concretely, when is it true that $$f:A \to B$$ is homotopic to a holomorphic function $$g:A \to B$$ where the homotopy $$H(x,s):A \times [0,1] \to B$$ satifies that $$H(C,s)=D$$ for all $$s \in [0,1]$$?

Also, if the question is too broad and depends on the particular cases: I ask for a reference where this type of problem is worked out (at least under some restrictions).