  Instantons on the Taub-NUT space are related to `bow solutions' via a
generalization of the ADHM-Nahm transform. Both are related to complex
geometry, either via the twistor transform or via the Kobayashi-Hitchin
correspondence. We explore various aspects of this complex geometry, exhibiting
equivalences. For both the instanton and the bow solution we produce two monads
encoding each of them respectively. Identifying these monads we establish the
one-to-one correspondence between the instanton and the bow solution.
