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The XMM discovery of a ms pulsar swinging between an accretion-powered (X- ray)and a rotation-powered (radio) pulsar state demonstrated that transitionsbetween the two states can be observed over timescales of a few weeks. Wepropose an XMM/NuStar ToO observation of 60 ks aimed at studying the accretionstate of transitional ms pulsars detecting X-ray accretion powered pulsationsand characterizing its variability over three decades in energy. Candidates arerestricted to black widows and redbacks systems in an evolutionary phase thatallows state transitions. Enlarging the number of systems in this transitionalphase is crucial to test binary evolution theories and to study the disk-fieldinteraction over a large range of mass accretion rates. [truncated! Please see actual data for full text]