  In order to construct a catalogue of oxygen-rich (noted M) asymptotic giant
branch (AGB) stars in the halo, complementing those of carbon-rich (C) stars,
previous lists of Miras and SRa semiregulars located in the nor thern
hemisphere are merged and cleaned of various defects. After putting aside known
C stars, characteristics lik e colours and periods indicate that most of the
remaining objects are M stars. Distances are obtained through the pe
riod-luminosity relation. By considering their position in the sky, stars lying
at $|Z| > 5$~kpc are confirmed to b e in majority in the Sgr tidal arms. The M
stars are more numerous than C ones. Our distance scale is supported by t wo
cool variables located in the Pal~4 globular cluster. Along the Sgr arms, there
is reasonable agreement on distan ces of our objects with recent RR Lyrae
distances. A few stars may be as distant as 150~kpc, with possibly four at t he
trailing arm apocenter, and two in the A16 substructure, 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. It contains $\sim$ 260
stars in the halo with $|Z| > 5$~kpc. Their $K_{\rm s}$ magnitudes range from 8
u p to 13. For comparison, the catalogue also provides $\sim 150$ stars in the
disc having $5$~$< K_{\rm s} <$~$8$. The catalog is available on request (NM)
before being on CDS.
