Few bands would regard playing six nights at the O2 as a step down. For U2, whose previous, stadium-filling 360° tour lasted two years and was the highest grossing tour of all time, this run of dates counts as positively intimate.

The Irish superstars are promoting their 13th studio album, last year’s Songs of Innocence, a record released in a welter of controversy. Ever welded to the grand gesture, the band dropped the album gratis into 500 million iTunes accounts, triggering some amusing over-reactions from malcontents self-righteously outraged at being given free music.

U2 have spoken of the album being the most personal of their near-40-year career, and its cathartic nature is sensitively reflected in this tour’s staging. The band begin the set spotlit under a single light bulb as they fire into a paean to their teenage musical epiphany, The Miracle (of Joey Ramone), and the punky The Electric Co from their 1980 debut album, Boy.

Bono has talked often of the devastating effect on his psyche of losing his mother to a cerebral aneurysm when he was 14, and new track Iris (Hold Me Close) is not so much a song as primal scream therapy delivered from an arena-rock stage. He croons Cedarwood Road, about his boyhood street, from an elevated metal cage among video projections that make him appear to be walking down that very street.

Few bands would regard playing six nights at the O2 as a step down. For U2, whose previous, stadium-filling 360° tour lasted two years and was the highest grossing tour of all time, this run of dates counts as positively intimate.

The Irish superstars are promoting their 13th studio album, last year’s Songs of Innocence, a record released in a welter of controversy. Ever welded to the grand gesture, the band dropped the album gratis into 500 million iTunes accounts, triggering some amusing over-reactions from malcontents self-righteously outraged at being given free music.

U2 have spoken of the album being the most personal of their near-40-year career, and its cathartic nature is sensitively reflected in this tour’s staging. The band begin the set spotlit under a single light bulb as they fire into a paean to their teenage musical epiphany, The Miracle (of Joey Ramone), and the punky The Electric Co from their 1980 debut album, Boy.

Bono has talked often of the devastating effect on his psyche of losing his mother to a cerebral aneurysm when he was 14, and new track Iris (Hold Me Close) is not so much a song as primal scream therapy delivered from an arena-rock stage. He croons Cedarwood Road, about his boyhood street, from an elevated metal cage among video projections that make him appear to be walking down that very street.

U2’s flirtations with technology have always veered from the cutting-edge to the cheesy, a trend continued as they pull a woman from the crowd to film Elevation: the shaky footage becomes a simultaneous live stream for subscribers to a mobile video app. More effective is Every Breaking Wave, a melancholy ballad sighed by Bono accompanied only by The Edge on piano.

U2 would not be U2 if they did not compulsively meld the personal and the political, and October is accompanied by harrowing images of the devastation being wrought by the bombing of Syria. Fleeing migrants and Isis training camps illustrate Bullet the Blue Sky, as Bono recites the complaints of critics of his global activism: “You’re part of the problem, not the solution.”

A set-closing greatest-hits run of the earnest Where the Streets Have No Name, Pride (In the Name of Love) and With or Without You harks back to the days when U2’s sole aim was to write colossal, insatiable pop songs. Then, a recorded introduction by Stephen Hawking leads into an encore that climaxes with the sumptuous, lovelorn One, still the most visceral love song that the band have ever penned. Even in minimalist (for them), stripped-down mode, U2’s defiantly ambitious, meticulously choreographed live productions put virtually every other rock band to shame.