MILAN, Feb 12 (Reuters) - Shares in Italian luxury shoemaker Tod's jumped on Monday and those of oil refiner Saras slumped after the two received buyout offers over the weekend, with both preparing to join peers that have left the Milan bourse.

The dwindling capitalisation of Italy's stock exchange and a steady flow of firms relocating abroad has become a hot topic in Italy, with listing professionals and large foreign investors criticising planned government measures to stem the trend.

Shares in Tod's rose 17.4% after private equity firm L Catterton offered to buy 36% of the group and take it private, in agreement with the Della Valle founding family.

By contrast, shares in Saras fell 6% to trade below the 1.75 euros ($1.88) per share offered by commodity trader Vitol to acquire the Moratti family's stake in the oil refiner and buy out other investors to take it private.

Saras' main asset is the 300,000 barrel-per-day Sarroch refinery in Sardinia, the biggest plant in the Mediterranean, whose location has grown in importance in light of the Red Sea route disruption.

"Saras's business is highly complementary to Vitol's core operations, and this transaction will strengthen European energy security and enhance supply for a key European energy asset,” Vitol CEO Russell Hardy said in a statement.

Unlike the Morattis, the Della Valle brothers will retain control of Tod's with a 54% stake, while they will tender another 10.45% stake.

LVMH, backer of L Catterton and a longstanding Tod's shareholder, will also keep its 10% stake. L Catterton will own the remainder of Tod's if the offer is successful.

L Catterton has said that if its 43 euro-a-share bid fails to meet the necessary threshold, it will still delist Tod's by merging it into the offer vehicle.

Shares had risen to 42.6 euros each by 0935 GMT, just below the price of the bid, which values Tod's at just over 1.4 billion euros.

A previous attempt in 2022 by the Della Valles to take Tod's private and manage its diverse brands separately fell through, but analysts said this time the prospect of the delisting was credible.

In addition to the eponymous brand, famous for its Gommino loafers, Tod's also owns the Roger Vivier shoe brand and the Fay and Hogan labels.

Citi analysts said shareholders may think that the bid price, which is only 7.5% above the failed 2022 offer price, does not fully reflect the ongoing turnaround of the Tod's brand and undervalues Roger Vivier.

However, broker Equita said the alliance between majority and minority shareholders in Tod's lent credibility to the threat that investors who snub the bid will end up with stock in an unlisted group.

($1 = 0.9285 euros) (Writing by Valentina Za; Editing by Jan Harvey)