You could imagine them popping out to a Finnieston cafe together to put the world to rights over a frothy cappuccino, or perhaps meeting up for a Friday night Scrabble match in Bute House.
Their political tussles are usually underpinned with a sense of unconditional – if not love, at least a base sense of liking and respect. Whatever the rhetoric between them, there is not usually real anger behind it. Their tiffs are more akin to a family disagreement.
And First Minister’s Questions began as usual, with Mr Sarwar arguing Sweden now owns a larger part in Scotland’s seabed estate than Scotland.
Ms Sturgeon retorted with a typical independence dig, pointing out Sweden has full control over its own energy.
"That's a matter Mr Sarwar might want to reflect on a little bit more every day,” she quipped.
Then, suddenly, the mood changed. Like someone worn down by a bad marriage that has gone on for too long, Ms Sturgeon turned personal, accusing Mr Sarwar and his party of wanting to “gurn” “and be negative” in the face of a positive development for Scotland.
But she didn't leave it there.
"That is what's characterised Scottish Labour for a long time,” she said, twisting the knife. “And it's why they’re sitting over there these days,” she added, before gesturing to the opposition benches. “Not there and certainly not here.”
Mr Sarwar went on to accuse the First Minister of having – turning one of her own favourite phrases on her – “a brass neck” in accusing the Tory party of having bad human rights values, but disregarding human rights when it came to economic gain over wind projects.
His comments seemed to leave Ms Sturgeon, for once, struggling for words, which, when they came, accused Mr Sarwar of the “political desperation” she said she had been expecting to hear from beleaguered Scottish Tory leader Douglas Ross.
"I’m just sitting here reflecting, almost unbelievably actually, that Anas Sarwar has just accused me of behaving like a Tory, the day after his party threw open the doors to a Tory MP,” she said, referring to MP Christian Wakeford’s defection in Westminster. “There is now so little difference between Labour and the Tories that their MPs are just so interchangeable."
With the recent goings-on at Westminster, “behaving like a Tory” is possibly one of the worst political insults anyone could throw at the moment.
Yet the scent of “political desperation” could be detected across Holyrood – not just on the Tory and Labour bench, but among the SNP-ers too. Change is in the air, with Labour polling its highest share of the vote since 2013, and, while the nationalists might not like it, what happens down south could well have a knock-on effect on the political make-up of Scotland.
Perhaps Mr Sarwar should, as Ms Sturgeon advised, spend the rest of the day polishing his brass neck. He may well need it soon.