  We present general relativistic numerical simulations of binary neutron star
(BNS) mergers with different initial spin configurations. We focus on models
with stars of mass 1.4 M_sol each, which employ the equation of state (EOS) by
Shen, Horowitz, and Teige, and which result in stable NSs as merger remnants.
For comparison, we consider two irrotational equal mass (M=1.35 M_sol) and
unequal mass (M=1.29,1.42 M_sol) BNS models using the APR4 EOS, which result in
a supramassive merger remnant. We present visualizations of the fluid flow and
temperature distribution and find a strong impact of the spin on vortex
structure and nonaxisymmetric deformation. We compute the radial mass
distribution and the rotation profile in the equatorial plane using recently
developed measures independent of spatial gauge, revealing slowly rotating
cores that can be well approximated by the cores of spherical stars. We also
study the influence of the spin on the inspiral phase and the gravitational
wave (GW) signal. Using a newly developed analysis method, we further show that
gravitational waveforms from BNS mergers can exhibit one or more phase jumps
after merger, which occur together with minima of the strain amplitude. We
provide a natural explanation in terms of the remnant's quadrupole moment, and
show that cancellation effects due to phase jumps can have a strong impact on
the GW power spectrum. Finally, we discuss the impact of the spin on the amount
of ejected matter.
