  Following Bachmann's recent work on bi-brackets and multiple Eisenstein
series, Zudilin introduced the notion of multiple q-zeta brackets, which
provides a q-analog of multiple zeta values possessing both shuffle as well as
quasi-shuffle relations. The corresponding products are related in terms of
duality. In this work we study Zudilin's duality construction in the context of
classical multiple zeta values as well as various q-analogs of multiple zeta
values. Regarding the former we identify the derivation relation of order two
with a Hoffman-Ohno type relation. Then we describe relations between the
Ohno-Okuda-Zudilin q-multiple zeta values and the Schlesinger-Zudilin
q-multiple zeta values.
