From left: Raheem Sterling of Chelsea, Christian Eriksen of Manchester United, Richarlison of Tottenham and Gabriel Jesus of Arsenal are among the biggest signings so far in the English Premier League's summer transfer window. (PHOTOS AFP / AP)

LONDON－Desperate to close the gap on Manchester City and Liverpool at the top of the English Premier League, Chelsea, Tottenham, Arsenal and Manchester United have spent the offseason aggressively pursuing new recruits with varying degrees of success.

All four have little margin for error if they are to have any hope of rivalling champion City and perennial contender Liverpool in the title race.

But even if the top two pull away once more, another tight race is expected for the final two lucrative places in the Champions League.

AFP Sport looks at how the battle for the top four is shaping up.

Chelsea

Charged with ensuring Chelsea's new era gets off to a flying start, Blues boss Thomas Tuchel has showed signs of feeling the heat during his club's hectic summer.

With former owner Roman Abramovich's lieutenants all swept away as part of the house-cleaning at Stamford Bridge, Tuchel took on more responsibility as the German worked with new co-owner Todd Boehly on overhauling his squad.

First impressions have been mixed, with Boehly flirting with a move for Cristiano Ronaldo before Tuchel demurred at the prospect of handling the volatile Manchester United star.

Raheem Sterling became Chelsea's first signing of the Boehly era after a 47.5-million-pound ($57.8-million) move from City, but the England international has been the only addition to the attack as Tuchel looks set to start the season without a natural striker after Romelu Lukaku was sent back to Inter Milan on loan.

Instead, Chelsea's focus has been on replacing centerbacks Antonio Rudiger and Andreas Christensen, who joined Real Madrid and Barcelona respectively on free transfers.

The Blues paid 33 million pounds for Napoli's Kalidou Koulibaly and have reportedly reached an agreement to sign Brighton's Marc Cucurella for 50 million pounds.

Tuchel has also been growing frustrated with unsettled quartet Cesar Azpilicueta, Marcos Alonso, Timo Werner and Hakim Ziyech, questioning his team's commitment in a furious tirade after Chelsea's 4-0 defeat against Arsenal in a preseason friendly.

Manchester United

Erik ten Hag's first preseason as United manager has been overshadowed by Ronaldo's demand to leave Old Trafford.

The studious Ten Hag is said to have impressed his squad with his attention to detail and intense training sessions since arriving from Ajax in May.

But the Dutchman's ability to lift United from the depths of its dismal sixth-place finish last season could hinge on how he handles the fallout from Ronaldo's bombshell.

The Portugal striker wants to join a club competing in the Champions League and missed United's preseason tour to Thailand and Australia for "family reasons".

Losing a player with Ronaldo's lethal instincts in front of goal is not the way Ten Hag would prefer to begin his time in Manchester, but he may eventually feel the departure of such a demanding superstar would be addition by subtraction.

Adding to Ten Hag's woes, United has found it impossible to land his top target－Barcelona midfielder Frenkie de Jong.

Instead, it has settled for Denmark midfielder Christian Eriksen, Argentina's Lisandro Martinez－the Premier League's shortest centerback at 5-foot-9 (1.75 meters)－and Dutch leftback Tyrell Malacia.

A return to the top four cannot be guaranteed against such a troubled backdrop.

Tottenham and Arsenal

In north London, Tottenham and Arsenal have been engaged in a frenzied battle for local supremacy which reached a dramatic conclusion last season.

Tottenham knocked Arsenal out of the top four in the penultimate game of the season after reeling in Mikel Arteta's side with a blistering run that included a 3-0 win over the Gunners.

Spurs manager Antonio Conte's response to achieving what he described as a "miracle" in qualifying for the Champions League was to demand Tottenham chairman Daniel Levy loosens the purse strings, a request which has so far yielded the signings of Richarlison, Yves Bissouma, Djed Spence, Ivan Perisic and Fraser Forster.

Arsenal has reacted to the disappointment at how last season ended by splashing over 100 million pounds on new signings.

Arteta raided his former club City for Brazil striker Gabriel Jesus and Ukraine defender Oleksandr Zinchenko in deals worth a combined 75 million pounds.

Fabio Vieira, a 34-million-pound signing from Porto, arrives heralded as a potential future star.