  The Sivers effect in single hadron semi-inclusive deep inelastic scattering
(DIS) on a transversely polarized nucleon describes the modulation of the cross
section with the sine of the azimuthal angle between the produced hadron's
transverse momentum and the nucleon spin ($\boldsymbol{P}_h$ and $\varphi_S$
respectively). This effect is attributed to the so-called Sivers parton
distribution function of the nucleon. We employ a simple phenomenological
parton model to derive the relevant cross section for two-hadron production in
semi-inclusive deep inelastic scattering including the Sivers effect. We show
that the Sivers effect can be observed in such process as sine modulations
involving the azimuthal angles $\varphi_T$ and $\varphi_R$ of both the total
and the relative transverse momenta of the hadron pair. The existence of the
modulation with respect to $\varphi_R$ is new. Finally, we employ a modified
version of the $\tt{LEPTO}$ Monte Carlo event generator that includes the
Sivers effect to estimate the size of single spin asymmetries corresponding to
these modulations. We show that $\sin(\varphi_R-\varphi_S)$ modulations can be
significant, especially if we impose asymmetric cuts on the momenta of the
hadrons in the pairs.
