A catalogue of oxygen-rich pulsating giants in the galactic halo and the Sagittarius stream

10 pages, 12 figs, 3 Tables. Accepted for publication by AAInternational audienceTo construct a catalogue of oxygen-rich (M) asymptotic giant branch (AGB) stars in the halo, complementing the catalogues of carbon-rich (C) stars, previous lists of Miras and SRa semi-regulars located in the northern hemisphere are merged and cleaned of various defects. After putting aside known C stars, characteristics such as colours and periods indicate that most of the remaining objects are M stars. Distances are obtained through the period-luminosity relation. By considering their position in the sky, stars lying at |Z| > 5 kpc are confirmed to be in majority in the Sgr tidal arms. The M stars are more numerous than C ones. Our distance scale is supported by two cool variables located in the Pal 4 globular cluster. Along the Sgr arms, there is reasonable agreement on distances of our objects with recent RR Lyrae distances. A few stars may be as distant as 150 kpc, with possibly four at the trailing arm apocentre, and two in the A16 sub-structure, angularly close to two C stars. Ninety radial velocities are collected from Gaia and other sources. A catalogue with 417 M pulsating AGB stars is provided. This catalogue contains ∼260 stars in the halo with |Z| > 5 kpc. Their Ks magnitudes range from 8 up to 13. For comparison, the catalogue also provides ∼150 stars in the disc having 5 < Ks < 8