  The algebra of big zeta values we introduce in this paper is an intermediate
object between multiple zeta values and periods of the multiple zeta motive. It
consists of number series generalizing multiple zeta values, the simplest
examples, which are not multiple zeta series, are Tornheim sums. We show that
convergent big zeta values are periods of the moduli space of stable curves of
genus zero on one hand and multiple zeta values on the other hand. It gives an
alternative way to prove that any such period may be expressed as a rational
linear combination of multiple zeta values and a simple algorithm for finding
such an expression.
